{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Active Subspaces Tutorial\n",
    "\n",
    "In this tutorial, we'll show you how to utilize active subspaces for dimension reduction with the [Python Active-Subspaces Utility Library](https://github.com/paulcon/active_subspaces). We'll demonstrate how to construct active subspaces with various components available and how to use the subspace to construct and use a response surface.\n",
    "\n",
    "We examine the following circumstances in constructing subspaces:\n",
    "1. You have only an interface to the function returning the quantity of interest, $f$.\n",
    "2. You have access to the function $f$ and its gradient with respect to normalized inputs, $\\nabla f$.\n",
    "\n",
    "The function we use for demonstration is (as seen on [http://www.sfu.ca/~ssurjano/wingweight.html](http://www.sfu.ca/~ssurjano/wingweight.html)):\n",
    "\n",
    "$$\n",
    "f = 0.036\\ S_w^{0.758}W_{fw}^{0.0035}\\left(\\frac{A}{\\cos^2(\\Lambda)}\\right)^{0.6}q^{0.006}\\lambda^{0.04}\\left(\\frac{100t_c}{\\cos(\\Lambda)}\\right)^{-0.3}(N_zW_{dg})^{0.49}+S_wW_p,\n",
    "$$\n",
    "\n",
    "and its inputs (and distributions) are summarized below.\n",
    "\n",
    "Variable|Symbol|Distribution (U(min, max))\n",
    ":-----|:-----:|:-----\n",
    "wing area|$S_w$|U(150, 200)\n",
    "weight of fuel in the wing|$W_{fw}$|U(220, 300)\n",
    "aspect ratio|$A$|U(6, 10)\n",
    "quarter-chord sweep|$\\Lambda$|U(-10, 10)\n",
    "dynamic pressure at cruise|$q$|U(16, 45)\n",
    "taper ratio|$\\lambda$|U(0.5, 1)\n",
    "aerofoil thickness to chord ratio|$t_c$|U(0.08, 0.18)\n",
    "ultimate load factor|$N_z$|U(2.5, 6)\n",
    "flight design gross weight|$W_{dg}$|U(1700, 2500)\n",
    "paint weight|$W_p$|U(0.025, 0.08)\n",
    "\n",
    "The first scenario we describe is when you have access to the function, $f$, but not its gradient (the file 'wing_functions.py' contains $f$ as defined above and its analytical gradient (wing and wing_grad, respectively), but for demonstration we initially pretend we don't have gradients). In this scenario, you have 3 options: use a global linear model to approximate gradients, use a global quadratic model to approximate gradients, or use local linear models to approximate gradients. We demonstrate each in turn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import active_subspaces as ac\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from wing_functions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first draw a set of inputs from the parameter space according to the distributions in the table above and compute the function's value at each of these points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "M = 1000 #This is the number of data points to use\n",
    "\n",
    "#Sample the input space according to the distributions in the table above\n",
    "Sw = np.random.uniform(150, 200, (M, 1))\n",
    "Wfw = np.random.uniform(220, 300, (M, 1))\n",
    "A = np.random.uniform(6, 10, (M, 1))\n",
    "L = np.random.uniform(-10, 10, (M, 1))\n",
    "q = np.random.uniform(16, 45, (M, 1))\n",
    "l = np.random.uniform(.5, 1, (M, 1))\n",
    "tc = np.random.uniform(.08, .18, (M, 1))\n",
    "Nz = np.random.uniform(2.5, 6, (M, 1))\n",
    "Wdg = np.random.uniform(1700, 2500, (M, 1))\n",
    "Wp = np.random.uniform(.025, .08, (M, 1))\n",
    "\n",
    "#The input matrix\n",
    "x = np.hstack((Sw, Wfw, A, L, q, l, tc, Nz, Wdg, Wp))\n",
    "\n",
    "#The function's output\n",
    "f = wing(x)\n",
    "\n",
    "#Upper and lower limits for inputs\n",
    "ub = np.array([150, 220, 6, -10, 16, .5, .08, 2.5, 1700, .025]).reshape((1, 10))\n",
    "lb = np.array([200, 300, 10, 10, 45, 1, .18, 6, 2500, .08]).reshape((1, 10))\n",
    "\n",
    "#We normalize the inputs to the interval [-1, 1]: \n",
    "XX = 2.*(x - lb)/(ub - lb) - 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell instantiates a subspace object and computes the active subspace by fitting a global linear model (this is indicated by the 'sstype='OLS'' flag). The 'nboot=100' flag says to use 100 bootstrap replicates to estimate variability in eigenvalue and subspace error estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Instantiate a subspace object\n",
    "ss = ac.subspaces.Subspaces()\n",
    "\n",
    "#Compute the subspace with a global linear model (sstype='OLS') and 100 bootstrap replicates\n",
    "ss.compute(X=XX, f=f, nboot=100, sstype='OLS')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot estimated eigenvalues, subspace errors, and a sufficient summary plot (a plot of the active variable vs data values)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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U1dV5nMYYY+KfFUxHRHsc/4IL/JMgqSpbtmzxNEtLuZTHpSzgVh6XsoBbeVzK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\nY4wxQbCCaYwxxgTBCqYxxhgThP8PY7ikQx5ohPoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110277c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mO3fuHCtXriQ8PJxZs2bx6KOPur3L1MjrzdfXlx9++IG77rqLhg0buqzbvSz+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\nnlNK7VFKJSulEpRSfyilhjgvpudISUnh448/5vn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jgL+JiOsj4jRSD29zUt8M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\nsxIXRjMzs5L/D1s9gxxctVYkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fc8cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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JSHVrOJf5bcSRJqMz+wSiMbvSedZK4MfO/dHU8N57uzjrrEsIBuPPpWaD21Ab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\nYYqIiORAFaaIiEgO/hfVLJ5pBiTdswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fd45e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#This plots the eigenvalues (ss.eigenvals) with bootstrap ranges (ss.e_br)\n",
    "ac.utils.plotters.eigenvalues(ss.eigenvals, ss.e_br)\n",
    "\n",
    "#This plots subspace errors with bootstrap ranges (all contained in ss.sub_br)\n",
    "ac.utils.plotters.subspace_errors(ss.sub_br)\n",
    "\n",
    "#This makes sufficient summary plots with the active variables (XX.dot(ss.W1)) and output (f)\n",
    "ac.utils.plotters.sufficient_summary(XX.dot(ss.W1), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now make the same plots with a global quadratic model (sstype='QPHD')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2ZRGxK49NWUTsyuOuCwXWDFvHGCOBg0AvEXnXvX0K0F1EOpagbbHl+yytnJwc4uLi2L17\nN3feeSfPPvtssCMppVS5U+7GGEXkJLAceNwY08YY0xeYAMwvaZu2PHaqtEJCQpg/3/VjeO655zhy\n5EiQEymlVPmRVs4eO5X/lG488Amu2zkeB5JE5LWSNm7LY6f8UZyvueYaLrrINR/CoEGDgp7HX2zK\nAnblsSkL2JXHpixgVx6bsoAdeRKK8dgpawqjiDjEPR2ce/mkiNwpItVEpKGIlPhssaIxxrB48WIA\nVq5cya+//hrkREopVXFYM8YYSBVpjNFT27Zt+c9//kPXrl155513gh1HKaXKjcLGGLUwlmP/+c9/\naNu2LQC7du2iSZMmQU6klFLlQ7m7+CYQbLn4xp8ZLr/88rxx07/97W9Bz1NaNmUBu/LYlAXsymNT\nFrArj01ZwI485e3im4Cy5eIbf1u4cCEAW7du5fPPPw9yGqWUsltxLr7RrtQKoG/fvqxatYrmzZvz\nzTffBDuOUkpZT8cYK3hh3LlzJ02bNgXgvffeo0OHDkFOpJRSdtMxRosEoo89Li6O/v37A3DrrbcG\nPU9J2ZQF7MpjUxawK49NWcCuPDZlAfvyeKOFsYKYM2cOISEh/PTTT6xZsybYcZRSqtzSrtQKZOjQ\noSxdupRatWpx4MCBYMdRSilraVcq9tyuEUgzZswgNDSUgwcPkpqaGuw4SillHb1dw4Mtt2sEsjjX\nrl2bUaNGAXD33XdTnLNkm/5YsCkL2JXHpixgVx6bsoBdeWzKAnbkKVdzpSr/SExMJDw8nIyMjLz5\nVJVSShWfjjFWQElJSSQnJxMWFobT6cSYArvRlVKq0tIxxkpm4sSJVK1alVOnTjF16tRgx1FKqXJF\nC2MZK4s+9qioqLw+9KlTp3L69Omg5ikum7KAXXlsygJ25bEpC9iVx6YsYF8eb7QwVlCjR4+mRo0a\n5OTkcO+99wY7jlJKlRs6xliBLVmyhGHDhgFw4sQJIiMjg5xIKaXsoGOMldRdd91F3bp1ARgxYkSQ\n0yilVPmghbGMlWUfu8Ph4NFHHwVg2bJlHDlyJKh5imJTFrArj01ZwK48NmUBu/LYlAXsy+ONFsYK\nrn///jRq1AiAO++8M8hplFLKfpVmjDExMZGEhAQrZr8pa6tXr+aaa64BID09nfr16wc5kVJKBUda\nWhppaWkkJyfr8xgrw/fpjYjQvHlzvvvuO7p27co777wT7EhKKRVUevGNRYLRx26M4amnngJg48aN\n7Nq1K6h5vLEpC9iVx6YsYFcem7KAXXlsygL25fGmXBdGY0y4MeYlY0yaMWaLMebyYGeyVUJCAvHx\n8QDccsstQU6jlFL2KtddqcaYEUBdEUkyxlwIPC8iVxSwX6XuSs31ySefcPnlrr8dJk6cyOeff47T\n6SQiIoLevXszZMgQIiIigpxSKaUCr7CuVGsKozEmHNgKjBGRje51YcBioB/gBOaJyByPY6oCIiIn\njDEXA4tFpEsBbWthdGvatCk7d+48a73D4SAuLo5JkyZx++23ByGZUkqVHevHGN1F8UXgonyb5gJt\nga7AMGCyMebm3I0ictxdFGsDy4HkMopcYsHsY09NTeXQoUMFbsvOzmbHjh1MmDAhaA85tm38waY8\nNmUBu/LYlAXsymNTFrAvjzdBL4zGmBbAR8D5+dZHAYOBsSKyTURWAbOBe/LtdyHwb2CKiKSVSehy\nyOl0MmPGDK+FMdeBAweYMWMGmZmZZZRMKaXsEvSuVGPMcCAOmAycALqJyEZjTHvgPSBKRE659+0M\nvOVeJ8aYRsAG4HYR2VrIe1T6rtRFixYxbtw4srOzi9zX4XCwYMECRo4cWQbJlFKq7FndlSoiT4rI\nvSLizLepPnAotyi6/QaEAXXcy5OBqsBsY8wmY8xLgU9cPq1du7ZYRRFc3aqrV68OcCKllLJT0Atj\nIaKA/P15ucvhACIyTETOE5GuItJFRP5WpglLIFh97E5n/r87CheMrlTbxh9symNTFrArj01ZwK48\nNmUB+/J4ExrsAIVw4i6AHnKXT/ja2MCBA2ncuDEA1atXJz4+Pm96uNwPqyIvHz9+HF/s2LGDkydP\nEhkZWWZ5c9nw87Itz7Zt24L+87A1z7Zt24L6/rbn0WXXcu7Xe/bsoShBH2P0ZIzJ4cwxxneBSBE5\n7d6eAKwFokUkx4d2dYzRhzHGXA6Hg7/+9a/MnTuXli1bBjCdUkqVLavHGAuxDTgFeN6w3xH4ry9F\nUbkMGTKEuLi4Yu9ftWpVsrOz2bBhA3/+858577zzWLRoEadPnw5gSqWUCj5rC6OInMR1b+Ljxpg2\nxpi+wARgfnCTlU7+brqyEhERweTJk6ldu3ah+9WuXZsnnniCqVOn0qBBA2JiYggJCeGnn35i9OjR\nVK1alZtuuokff/zR7xmD9bPxxqY8NmUBu/LYlAXsymNTFrAvjze2Fcb8/Z3jgU+Ad4DHgSQRea0k\nDSclJZWbDyVQbrvtNlJSUmjWrBkOh+OMbQ6Hg2bNmpGSksLw4cMZP348P/30E2+88QY9e/YkPDyc\nqKgoTp06xauvvkrjxo1p1qwZK1asoLJ3Uyulyo+0tDSSkpIK3ceqMcZA0THGM2VmZrJ06VLWrFlD\nZmYm4eHh9OnTh8GDBxMenv96J5d9+/axZMkSFi5cSFZWFhkZGXkFMSoqiltuuYWHH36YWrVqleW3\nopRSJVIu5koNJC2M/nP69GnWrl3LnDlz2Lp1KyKSd2uHMYZWrVoxc+ZMevXqFeSkSinlXXm9+KZC\nsq0719c8oaGh9O3bl/fee4+vvvqKkSNHEhMTQ0xMDCLCtm3b6N27NzVq1GD8+PE+3SZS3n82gWRT\nFrArj01ZwK48NmUB+/J4o4VRlViTJk1ISUnhwIEDPPXUU7Rq1YqIiAiqVKnCkSNHmDdvHtWqVaND\nhw589NFHBbbhdDpZtGgRvXr1YuzYsfTq1YtFixb5PCGBUkr5jYhU+BcgiYmJsmnTJlGB9cUXX8jg\nwYMlMjJSqlatKrguqBJA6tSpI1OnTpVTp06JiMjy5culWbNm4nA4ztjP4XBIs2bNZPny5UH+bpRS\nFc2mTZskMTFRXOWv4JqhY4wqIDIyMlixYgVz5swhPT2dzMxMcnJct586HA5atGhBenp6oU/7qF27\nNikpKfp8SKWU3+kYo0Vs62MPVJ7o6GiGDRvG999/z6ZNm+jXrx/h4eFERkaSnZ3Nl19+af0jsGz6\nrGzKAnblsSkL2JXHpixgXx5vtDCqgDLG0LZtW1566SXS09OZOnUq1apVK/bxO3fu5Omnnw5gQqWU\nOpN2paoy17NnT9avX+/T/uvWrQtgIqVUZaNdqcoqvnaN6hWqSqmyVGkKoy1TwtmQwVMw8kRERPi0\n/+bNm7njjjvYv39/gBIVzKbPyqYsYFcem7KAXXlsygJ25CnOlHCVqjDmPp9LBVfv3r3Pmqu1MCJC\namoq9evXp127dmzZsiWA6ZRSFVlCQoLOlQo6xmgbp9NJfHw8O3bsKHLf2NhYnE4nISEhnDx5EnCN\nDdSrV48pU6YwePBgqlSpEujISqkKRscYlVV8eQTW4sWL+eWXX7jvvvuIiYkhOjoaEWHfvn3cfffd\nVKtWjWHDhvHrr7+WUXqlVEWnhbGM2dDH7ilYeYr7CKzbbruNc845h+TkZPbv309KSkrecyKNMTid\nTpYsWULDhg3p2LEjW7Zs8dtjsGz6rGzKAnblsSkL2JXHpixgXx5vtDCqoLn99tvZvn078+fPp2fP\nnsTHx9OzZ08WLFjA9u3bz5rxJiIigqFDh7J3715SU1Np1aoV0dHRVKlShezsbN5//306derEeeed\nx5IlS/RqVqVUiegYoyrXPvroI6ZNm8amTZswxnDixAnAddYZFhbGoEGDuP/++2nUqFGQkyqlbKLP\nY9TCWOHt3LmT2bNns2LFCsLCwjhy5Ajg+uUPDQ3liiuuIDk5mU6dOmFMgf8WlFKViF58YxHb+tht\nylOaLHFxcSxZsoQff/yRMWPGEBsbyznnnANAVlYWmzdvpmfPnpx33nk88cQTXp8T6fkYrPj4eGse\ng2XT5wR25bEpC9iVx6YsYF8eb7QwqgqlVq1aJCUlsW/fPqZPn07Dhg2pWbMmYWFhOJ1Ofv75Z8aP\nH0/t2rW55557+OGHH/KOTU1NJT4+nnHjxvHWW2+xfft23nrrLcaNG0d8fDypqalB/M6UUmVFu1JV\nhZadnc2qVauYPn0633//PTk5OWRkZABQpUoVHA4H7dq1o02bNjz//PMcOHDAa1tl/Rgsp9PJ0qVL\nWbt2LU6nk4iICHr37s2QIUN8nj1IKXUmHWPUwqiALVu2MHPmTNLS0oiIiOD3338HyBtzLM7vSLNm\nzdi+fTvh4eEBzZqamsqMGTPYuXMn2dnZeesdDgdxcXFMmjRJn1OpVCnoGCM6V6o3NuUJdJYrrriC\n1atX89lnn3HDDTdQtWpV6tWrl/fU7uIoi8dgpaamMmHCBHbs2HFGUQTXGfCOHTuYMGFCULt2K9Pv\nja9symNTFrAjT3HmStUzxjKWlpZm1ZytNuUp6yz79+9n8eLFzJo1i9OnTxf7OGMMMTExREREEBER\nQWRkJFFRUVStWpXo6GiqVatGTEwM1apVo3r16sTGxlKtWjWqVq161iv3uKpVqxIZGUlmZmaxp8sr\nq7PXglTm35ui2JTHpixgVx7tSrWoMCr7dO7cmXfffTeg72GMISQkBGPMWbeL5OTkkJOTg4jk/mMt\nVpsOh4MFCxYwcuTIQERWqkIrrDCGlnWYQDHGXAf0FZFBwc6iypeoqCif9q9ZsyYtW7YkOzubU6dO\ncerUKbKyssjMzCQrKytvnedLRM7qFi2IL3/AZWdns3r1ai2MSvlZhSiMxpjZQB/go2BnKYpNXQlg\nV55gZenduzdvv/12sQoXuK4W/fDDDxERoqOj87pCY2JiiIqKIioqisjIyLwu1qioKCIiIggLCyMs\nLIzQ0FBCQ0Pz5ojNLaZZWVmkpqby008/FTv73r17OXXqFGFhYSX63ktKf2+8symPTVnAvjzeWFUY\njTHhwFZgjIhsdK8LAxYD/QAnME9E5uQ79GNgDTCgDOOqCmLIkCE89thjPo/rZWZmcvTo0bNex44d\n4+jRoxw5coQjR45w+PBhfvnlF44cOZK3/dixY/zxxx+cPn36jDHH3Bl7iuvbb7+lVq1ajBw5knvu\nuYcGDRqU9MeglHKzZozRXRRfBK4FrvIojAuBzriKXiPgH8AQEXk53/GdgQEFdaXqGKMqyj/+8Q/G\njx9f5H2Mjz76KLfddpvf3jcrK+uMovr888/z2GOPkZOT41M7uRfgdO3alYkTJ9K5c2ed+k6pQhQ2\nxph3qXowX0AL4DP3Kxvo6l4fBZwAunjsOwl4t4A2OgPPemlflCrK8uXLpVmzZuJwOATIezkcDmnW\nrJksX7484BlOnjwpzZo1O+P9vb1q1KghI0aMkMaNG5+RNTo6Who3biyLFy+WY8eOBTyzUuWRuy4U\nWJNsuY+xM/AO0B7wrOCtgDDgA4917wNtTDn9c9iG+3g82ZQn2Fl8fQxWIBT3Ic6xsbHUqlWL119/\nnYSEBP7v//6P1q1bk52dTUZGBnv27GHKlCnUq1ePESNG8M033/g1Z7A/K082ZQG78tiUBezL440V\nhVFEnhSRe0Uk/0zN9YFDInLKY91vuIplnTILqCqN8PBw7rnnHtatW8e8efNYt24dI0eOLNN7BYvz\nEOdFixbx3XffsWbNGpxOJ4sXL6Zhw4ZMnTqVHj16EBYWxuHDhzlx4gQvvvgibdq0oWPHjrz++us+\n3bOpVGVkzRhjLmNMDtBNRDYaY24DZolII4/t5wM7gfNFZG8x2xTbvk+lipKZmcnSpUtZs2YNmZmZ\nhIeH06dPHwYPHnxWof7ll19YuHAhS5cu5ZJLLiEhIYHdu3ezZs0aDh8+DLhuS4mOjgZg1KhRDBky\nhLp165b596WUDcrVDf75CmM/4HERqeOxvTnwFVBXRA4Ws00ZMGAAjRs3BqB69erEx8fnXTace3qv\ny7pc3pczMjKYNGkSL7/8MjVq1KBnz57s2bOHDz/8kF9//RWAkJAQatasycmTJ+nTpw8dOnTg4osv\npkuXLkFqqOCLAAAgAElEQVTPr8u6HKjl3K/37NkDwLJly+y++MbzBeTwv4tv2gNZQKjH9gRcF+SE\n+NBmyUdo/WzTpk3BjnAGm/LYlEXErjy+Zjl9+rT861//kiuvvFLq1q0rAwcOlMmTJ0ubNm3OuICn\nQYMGUqtWLbn44ovl6aefluPHjwckTyDZlEXErjw2ZRGxKw/l4OIbb7YBp4ArPNZ1BP4rIr5dz65U\nJeJwOOjbty/vv/9+3jjkwoULOffcc5k2bRq9evUiLCyMX375hYMHD7J//35mzpxJgwYNGDduHDt3\n7jyrTc+HOI8dO9aahzgr5W9Wd6W6l5/AVQzvxHUxznLgLhF5zYc2xbbvU6myVtA45J49e1izZg2H\nDh0CIDo6mkaNGpGenk6bNm0YO3YsPXv25IUXXtDHYKkKpbyNMWZz5g3+kcDjwI3AMWCuiMz3sU1J\nTEwkISEhr99ZqcoqIyOD559/nkcffZSIiAh69eqV90DnH374AYDQ0FAuvPBCTpw4wbFjx8jMzOT4\n8eNe2yzrhzgrVVJpaWmkpaWRnJxcfsYYA/FCxxi9simPTVlE7MoTiCwFjUNOmTJF2rZtK8aYvHHI\nKlWqFGvCgWbNmonT6fR7zqLY9DmJ2JXHpiwiduWhHI8xKqUCpKBxyAULFlCvXj2mTZtGnz59cDgc\nZGVlFau9sniIs1Jlwbqu1EDQMUaliif/OGR6ejq7du0q9vE9e/Zk3bp1AUyolH8UNsZYac4Yk5KS\nzrifRSl1tgYNGvDII4+wd+9ebr75Zn7++Wefjs/MzAxQMqX8Iy0tjaSkpEL3qVSF0YYLb2wrzjbl\nsSkL2JWnrLNER0dzzz33+Pxvpiynzstl0+cEduWxKQvYkSchIUELo1Kq5K6++uqz5mv1xuFw0KdP\nnwAnUirwdIxRKeWV0+kkPj6+WA9xDg8PZ+/evdSpo/P7K/vpGKNSqkSK+xismJgYWrRoQZ8+fTh6\n9GgZpVMqMLQwljEb+tg92ZTHpixgV55gZinsMVi56tatS3JyMnXr1uWqq67i2LFjZZbPps8J7Mpj\nUxawL483WhiVUkUq6CHOLVu2pHbt2kRERLBz5042btzI0KFDqVu3Lt26dSvT4qiUP1WaMUadEk4p\n/8rOzqZly5Y0bdqUN998k8jISBYuXEjdunVZsmQJv/32G//+97+pVq1asKMqlac4U8L5VBiNMRcC\nv4nIUWNMN+B6YKuIPOefyIGhF98oFRhvvvkm48aNo27dunz44YdcdNFFzJw5k5CQEC2Oymp+ufjG\nGDMQ1wOC/2KM+TOwCrgQeNgYM9kfQSsD2/rYbcpjUxawK49NWeB/ea655hpq1KjBpZdeSs2aNfn6\n669ZuXIlxhiGDBlSJmOOtv5sbGBTFrAvjze+jDE+CAwWkTRgIPCViFwF9AeG+j+aUsp2xhhmz57N\nv/71L0aOHAnAihUr2LVrFyEhIQwZMoQ6deqU+QU5SpVGsbtSjTEngQtF5CdjzPdAqohMNcY0xlUk\nqwYuZuloV6pSgdWlSxcuvvjivOc7NmrUiPnz5xMWFkZOTg5Lly5l//79vP3229qtqqzgr/sYfwCu\nMsb0BC4A3nSvHwB8X7qISqny7JFHHuGVV17h1ltvpUGDBvz0008sW7YMIO/MsXbt2nrmqMoFXwpj\nIvAEsAb4l4hsM8bMw9XFqmOMxWRbH7tNeWzKAnblsSkLnJ3n8ssvp23btrzzzjtMmDABh8PBm2++\nyfbt2wFXcRw6dCi1a9eme/fufi2Otv9sgsmmLGBfHm+KXRhF5FWgIdBaRK53r14GtBCR1YEIp5Qq\nP2bNmsUbb7xBgwYN6N+/PwDz5s0jIyMD+F9xrFWrlt+Lo1L+5OvtGhHAjbiuRl0AtAK+EZFfAxPP\nP3SMUamy8fe//x2Am2++mfvvv58dO3bQqVMn7rvvvrx9cnJyeOqpp/j999/ZsGGDjjmqoPDX7Rpx\nwA5gKq7u0+q4rkb9yhjT2h9BlVLl2/Tp01mzZg0ZGRmMHz+eiIgI3n33XTZv3py3T0hICMOGDeOc\nc86he/fu/PHHH0FMrNTZfBljXAj8C4gDcp9GeivwCjDfz7kqLNv62G3KY1MWsCuPTVnAe57zzz+f\n/v378/rrr3PuuecyePBgAJ544gkOHDiQt59ncbzqqqtKVRzLy88mGGzKAvbl8caXwngFsNizT9L9\n9RzgL/4O5m9JSUnl5kNRqjxLTExk48aNHDx4kO7du9OmTRuOHz/O/PnzycnJydsvtzjWrFmz1MVR\nqeJKS0sr8kHFvtzH+DPwdxHZbIz5A2glIj8YY67FVTAblTZwoOgYo1Jla+LEiXz11VeMGDGCw4cP\nM2rUKI4ePcrgwYO59tprz9g3JyeHJ598kkOHDvH2228TExMTpNSqMvHXfYxPAk+5C6EBWhhjhgBL\ngGdKH1MpVVE88MADfPTRR6Snp1OjRg1GjRoFwLJly/jxxx/P2DckJIThw4dTs2ZNHXNUVvDldo3p\nwGPAIiAK11yp04AUXBfkqGKwrTvXpjw2ZQG78tiUBYrOU7NmTcaOHcs///lPANq2bUv37t3Jysoi\nJSWFrKysM/bPLY41atTwuTiWt59NWbIpC9iXxxufnscoIotE5DwgBqghIvVEZLaI5BR1bCAYl2eM\nMe8bY9YaY2oFI4dS6mzjxo3jyy+/ZPfu3QAMHjyYevXqsXv3blasWHHW/qUpjkr5ky9jjIMK2y4i\nz/olkQ+MMTcAXURklDHmZqCdiIwvYD8dY1QqCObPn89LL73EpEmTAPj222+5//77ERFmzpzJJZdc\nctYxuWOOhw8fZsOGDTrmqAKisDFGXwrj7nyrQoE6wGngAxHpXsqQ4cBWYIyIbHSvCwMWA/0AJzBP\nROZ4HJMCpInIKmNMNffXlxbQthZGpYIgMzOTCy64gDFjxtCiRQsA/vGPf/DSSy9Rp04dFi1aRFRU\n1FnH5eTk8MQTT3D06FHWr1+vxVH5nV8uvhGR8/O9GgE1gdeBtFIGDAdeBC7Kt2ku0BboCgwDJrvP\nDHNVA3LnlfoDiC5NjrJgWx+7TXlsygJ25bEpCxQ/T3h4OMnJybzwwgvk/nHav39/4uLi2L9/P089\n9VSBx4WEhDBixAhiY2Pp0aNHod2q5fVnUxZsygL25fHGpzHG/ETkOJAMjC1pG8aYFsBHwPn51kcB\ng4GxIrJNRFYBs4F7PHY7hmu8E/d/j5Y0h1IqMAYMGEBGRgafffYZAKGhoYwfP56wsDA2btzIBx98\nUOBxvhRHpfzJp7lSC2zAmJuAJ0XknBIePxzXbDqTgRNANxHZaIxpD7wHRInIKfe+nYG33OvEGNMP\n6CQio40x/YH2IjKmgPfQrlSlguiVV15hypQpzJkzB2NcvVerV6/mqaeeIiYmhsWLF1OzZs0Cj/Xs\nVt2wYQPR0dZ3DKlywF9zpb5njHk33+sz4AVgaUnDiciTInKviDjzbaoPHMotim6/AWG4xjbB1Y1b\n1RjzPq55W2eUNIdSKnBuvPFGwsLC2LJlS966q6++mksvvZQ//viDBQsW4O2PV88zx+7du+c9rUOp\nQPGlK/XfwDser38DLwE9ReSBAGSL4n9zsubKXQ4HEJEcEblLRDqISFcR2R+AHH5lWx+7TXlsygJ2\n5bEpC/ieJyQkhNmzZ/Piiy+SnZ0NuP5iHz16NDExMXz66aesXbu20OO9Fcfy/rMJJJuygH15vAkt\n7o4ikhzIIAVw4i6AHnKXT/ja2MCBA2ncuDEA1atXJz4+noSEBOB/H5YuB3c5l+Y5e3nbtm1B/3mU\nNk+PHj0499xzSU1NpXXr1rRs2ZJzzjmHPn368OKLL/Lss8/SqlUrDh8+DEDLli0B+OKLL/KWR4wY\nwfTp02nbti0ff/wx0dHRbNu2Leg/D89l2/Losms59+s9e/ZQlELHGI0xy4tswU1E7ijuvoW8Xw5n\njjG+C0SKyGn39gRgLRDty6QCOsaolB3ef/99br75Zh577DGqVKmSt37evHls3LiRuLg45syZQ2io\n97/Zc8ccjx07xvr163XMUZVIacYYs314+ds24BSup3rk6gj8N1gz7SilSqdDhw60bNmS9evXn7F+\n6NCh1KlTh507d/LSSy8V2kZut2pMTAw9evTQMUfld4UWRhG5s7gvfwcTkZPAcuBxY0wbY0xfYAIl\nfPajLY+dsiGDJ5vy2JQF7MpjUxYoXZ6HH36Y1157Dafzf9fbVa1albFjx2KM4eWXX+bbb78ttI2Q\nkBDuvvtuYmJiaNeunVW3ctj0WdmUBezIk5ZW9GOnfLkqNcQY088Yk2iMmep+TTPGzDbGvF3asG75\n+zvHA5/gutjncSBJRF4rScNJSUl5fc5KqeD5y1/+QkJCAqtXrz5jfcuWLbn++uvJycnh0Ucf5eTJ\nk4W2k1sco6OjadOmTZHFVClwjT3683mMjwN3Ap8BlwNbgAtwzX4zS0SsfcKGjjEqZZfvvvuOdu3a\n8fjjj58xRpiVlcX48ePZs2cPPXr04J577imkFRcRYcOGDaxYsYIlS5bQr1+/QEZXFYS/nsd4E64H\nFV8B7ARGAH8CXqUEV4kqpSqvCy+8kGuvvZaVK1eesb5KlSpMmDCB0NBQ1q9fz3/+858i2zLG0KNH\nD6ZMmcLo0aMZN27cWY+1UsoXvhTGari6NQG+ANq6rxZ9mDOnaVOFsKGP3ZNNeWzKAnblsSkL+CfP\n1KlTWb9+fd7tGbkaN27MgAEDAFi0aBFHjhwptJ3c2zmaNm3K3Llz2bJlCwkJCezbt6/UGUvCps/K\npixgXx5vfCmMu4DcJ1d8has7NbeNEk0HV5ZsufhGKeXSqFEjBgwYwKuvvnrWtr59+/LnP/+ZI0eO\nsHjxYq+z4uRXrVo1Jk2axPnnn89f/vIX3n33XX/HVuVccS6+8WWM8U7gMWAQsB34FHgeaA/sE5Fe\npcgaUDrGqJSdDhw4wIUXXsjcuXOpW7fuGdv279/P6NGjOX78OKNGjaJ79+4+tf3f//6XhQsX8uCD\nDzJhwoS8OVqVAv89duo54CrgOxH5BrgOqIXryRh+v11DKVXx1a5dm5EjRxZ472KdOnUYPnw4AEuX\nLvW5a7R169bMnj2bp59+mhtuuIFjx44VfZBS+Ha7xt3ADhH5FEBE1ovITSIyXER+DVjCCsa27lyb\n8tiUBezKY1MW8G+e++67j08//ZS9e/eeta1z58507NgRp9PJvHnz8uZZ9ZQ7xliQunXrMnPmTE6d\nOkXr1q356quv/JbbG5s+K5uygH15vPFljHEkkG6M2WCMGWSMiQ1UKKVU5REbG8vEiRP55z//edY2\nYwwjRozgnHPO4ZtvvuG113y/jTksLIwRI0Zw9dVX07FjR1544QV/xFYVmE/PYzTGXAL0w3XrxgXA\nBuCfwL/cDy22ko4xKmW3EydO0KRJE+6//36aNm161vZt27YxZcoUHA4Hc+fOJS4urkTv88MPPzB7\n9myuvfZa5s2bR1hYWGmjq3LKX/cxIiJfikiSiFyM6wrVz4AnAe1KVUqVWFRUFImJiV7P5uLj4+nb\nty/Z2dmkpKSQmZn/iXTF06RJE+bOnctnn31Gx44d+fnnn0sTW1VQPhVGAGNMjDHmVmAarinb9uK6\nl9FqttyuYUMGTzblsSkL2JXHpiwQmDx33XUXBw4c8DpmeMcdd9CoUSN+/vlnnnnmGVatWkViYiKj\nR48mMTGRVatWcerUqQKP9RQdHc0DDzxA8+bNufTSS9m4caNfvw+bPiubsoAdefw9V+pdxpg1wAFg\nKvAt0F5ELhGRGaUJWhZ0rlSl7BYWFsb06dNZsWJFgfcthoeHM2HCBEJCQli3bh1Lly7l008/Zffu\n3Xz66ac8/fTTjB49uliFLiQkhJtuuonRo0fzt7/9jZkzZ5KTow/tqQz8PVfqz8DLwD9FpOh5miyi\nY4xKlQ/Z2dm0bNmSfv36cfnll5+1fePGjTz++OOFdqXGxsYyaNAgunbtWqz3PHDgACkpKTRu3Jh/\n/OMfVK9evcT5VfnhrzHGRiIyvrwVRaVU+eFwOJg1axYvvvjiWWdwp06d4uWXXy5yfPHo0aO8/PLL\nxZ4vtXbt2kybNg2Hw8Gll17K559/XuL8qmLwpTDWMMbMMsb82xiz2RjzrucrYAkrGBv62D3ZlMem\nLGBXHpuyQGDz9O3bl9jYWN57770z1q9fv77YN/nv27fvrIchF6ZKlSoMGTKEG264gYSEBJYtW+ZT\nZk82fVY2ZQH78njjS2FMxTXDzXZgI65nJHq+lFKq1IwxzJ49m5deeonTp0/nrd+6dWuxxwFzcnL4\n5JNPit4xn4SEBKZNm8ZDDz3E0KFDS3z1qyrffBljPAl0EhHff9uCTMcYlSp/EhISuOSSS+jZsycA\n//d//1foLDf5tWzZkpkzZ5bovU+cOMGiRYs4ceIEK1eu5LzzzitRO8pe/hpj/BnQ6qKUKhOzZ8/m\nlVdeyTtrq1Klik/H+7q/p6ioKCZOnEh8fDytW7dmw4YNJW5LlT++FMb7gceNMb2NMc2NMU08X4EK\nWNHY1sduUx6bsoBdeWzKAmWT5/LLL+fyyy9n7dq1AFx22WWEhBTvf1khISG0adOmVO9vjOH6669n\n/Pjx/P3vfyc5OblYXbk2fVY2ZQH78njjS2F8FbgMWA18DXzvfu10/1cppfxq1qxZvPHGG5w4cYIe\nPXpQv379Yh1Xr149evTo4ZcMLVu2ZO7cubz22mv07t2bQ4cO+aVdZS9fxhj/VNh2EfnRL4kCQMcY\nlSq//v73v2OMoX///mzatIlnnnmGo0ePFnrMBRdcQEpKCg6Hw285Tp8+zfLly/nvf//LypUrufTS\nS4s+SFnLX89j/NFd/BoCXYFDQAzwq81FMZctU8IppXwzbdo01qxZw9GjR+nSpQuDBg2iQYMGZ3Wr\nhoSEUKdOHcLCwti1axcLFy7062w2oaGhDBo0iFtuuYVu3brx9NNP+61tVXaKMyWcL2eMdXB1o14M\nhAMXAo8Cfwa6i8jO0oQNJJvOGNPS0qyams6mPDZlAbvy2JQFyj7P8OHDOXDgAHfe6XomelZWFm+9\n9RZbt27l8OHD1KhRgzZt2tCjRw927drF5MmTyczMpG/fvgwePBhjCjwxKLGffvqJ2bNnk5CQwBNP\nPEFERETeNps+K5uygF15/HVV6iJgD1ALOOledxuu+xoXlSagUkoVJjExkXfeeYeDBw8CritOr7nm\nGpKTkxkyZAjJycn06dOHKlWq0Lx5cyZNmkRoaChvvvlmgc95LK1GjRoxe/Zs9uzZQ7t27di9e7ff\n30MFjy9njAdx3cf4tTHmD6CViPxgjGkOfCwiQX1wsTHmOqCviAwqYJs1Z4xKqZK57777+Prrrxkx\nYkSx9t+yZQuPPPIIOTk5DB06lGuuucbvmUSEVatW8frrr7N8+XJ69+7t9/dQgeGvM8YcIKqA9fUB\nZ0mC+YsxZjZQsjt5lVLlwoMPPsiHH35Ienp6sfa/4ooruOeeewBYsmSJ3x8vBa7/ufbt25eJEycy\naNAgJk+eTHZ2tt/fR5UtXwrjC8AiY0wrXDf6VzPGXAU8heupGyVijAk3xnxhjOnqsS7MGLPEGHPI\nGJNujLmviGY+Bor3Z2SQ2XYBkE15bMoCduWxKQsEJ0/NmjUZO3bsWV2jhc2Gc9VVV3HXXXcBsGDB\nAj7++OOAZLvooouYM2cOa9as4c9//jOvvvoqTmdQzxcA/b0pKV8K40RgC64iFA18CqwF/u3e5jNj\nTDjwInBRvk1zgba4rn4dBkw2xtzsrR0Rea0k76+UKl/GjRvHl19+6dOY3nXXXcfNN99MTk4Ojzzy\nSMCenlGjRg2SkpK46KKLmDVrFvXr12fIkCF8+OGHBT5fUtmr2GOMeQcYEwk0AUKBXSKSUaI3NqYF\nrrNQcF3ZepWIbDTGRAEHgatFZJN730lADxHp5F6eBnQA/hCRvu51nYEBOsaoVMU2f/58XnrpJSZN\nmlTsY0SEJ598krVr1xIZGcmMGTNo2rRpAFPC/v372bx5M5s3byYkJISBAwdyxx130Lhx44C+ryqe\nwsYYfbn4ppOXTQKcAvaJyF4fQg0H4oDJwAmgm7swtgfeA6JE5JR7387AW+51BQbWwqhU5eB0OomL\ni2PMmDG0aNGi2Mfl5OTw6KOPsnnzZmJiYnj44YfLZHJwEeH7778nLS2N999/n4suuohBgwbRr18/\nqlWrFvD3VwXz18U3z+B63FQasBJ4w/11GvAusMcY86ExplhzNonIkyJyr4jk74ivDxzKLYpuvwFh\nQB0f8lrJtj52m/LYlAXsymNTFghunoiICJKTk3nhhRcQkWI/cSMkJISxY8dy2WWX8ccff/DQQw/x\n22+/+T1f/jzGGC688EKGDh3KM888Q+fOnXn22Wdp2LAh/fv3Z/369QG7YEd/b0rGl8L4PPAJ0FxE\nzhGRmrjO+N4DJuEqWj8DC0uZKQrI/xC03OVwbweJyOaCzhaVUhXPgAED+OOPP/jss898Oi40NJQH\nHniAiy++mN9//50pU6Zw+PDhAKU8W5UqVWjfvj0PPPAATzzxBNWrV2fcuHE0aNCAe++9ly+//LLM\nsijvfOlKPYCru3N7vvWtgH+LSG33uOEWEanhUwhjcvhfV2o/4HERqeOxvTnwFVBXRA760rb7eBkw\nYEBe33716tWJj4/Pm4Eh968YXdZlXS4/y/v37+ehhx7ijjvuwBhDy5Ytgf+dsRW2fPLkSV544QV2\n7dpF3bp1GTp0KJdffnmxj/f38m+//UZ6ejqbN28mOjqaXr168dBDD1GnTh1rft7lfTn36z179gCw\nbNkyv4wxHgBuEZF/51vfDXhFRGq4C+MH7rPJYstXGNvj6pqNFJHT7u0JuK6AjRYRnyc/1DFGpSqe\nnJwc4uPjufrqq7nyyit9Pv7o0aPcf//9/PLLL7Ro0YKpU6eeMbVbMGRnZ/PFF1+wefNmPv74Y668\n8kruuusu+vTpE/RsFY0/xxiXGWPuMsa0MsbEG2PuAp4DnjfGnAPMxjXmWBrbcF3Mc4XHuo7Af0tS\nFG3j+deLDWzKY1MWsCuPTVnAjjwhISE88sgjPPfccyUao4uNjWXq1KnUqlWLb775hlmzZpGVlVXq\nXMUd8yyIw+EgPj6eMWPG8Mwzz9C8efNS3fphw+fkybY83vhSGB8EHgeSgc9w3ceYDCwG7sX1rMYs\nYGRpAonISWA5rocitzHG9AUmAPNL065SquLp2bMntWvX5rXXSnYrc506dZg2bRqxsbF8+umnpKSk\nWDNzTWRkJH/9619JTk4mJSWFU6dO0b9/f+Li4pg2bVpel6DyP5/vYwRwnx2eFpHCH4pW/Paycd/H\n6F6OxFWEbwSOAXNFpMSF0RgjiYmJJCQk5PU7K6UqhvT0dNq1a8d1111H9+7dS9TGzp07mTRpUt4D\nkUeOHOn3J3L4g4jw3Xffkea+9ePiiy/WWz98lJaWRlpaGsnJySUbYzTGDAJWiEim+2uvROTZ0sUN\nHB1jVKpi+/777+nQoQODBw+mffv2JWrjyy+/JDExkVOnTnHjjTcycOBA/4b0s6ysLLZu3crmzZv5\n/PPP6d27N3feeSfdunXz6wOaK6rSjDFOwTX9W+7X3l6T/RO14rOtj92mPDZlAbvy2JQF7MqTlpZG\n06ZNWbduHU8++WSJx/guueQSHnjgARwOB6+99hqvvvpqidopzRijL/Lf+hEbG8vYsWPPuPXDps8J\n7Pq9KUxoEdvH4urKRETOL2gHY0wMruKolFJBc+mll/Lqq6/Sr18/pkyZQlxcnM9ttGnThnHjxpGS\nksKyZcuoWrUqvXr1CkBa/4qNjeWaa67hmmuuYe/evaSlpfHXv/6V6OhobrvtNjp16kS7du2oWrVq\nsKOWC0V1pWYD9UVkv8e6vUBHEfnRvVwXSBcRa8/dtStVqcrjtddeY/jw4cyYMYNzzz23RG2sXbuW\nJ554AmMM9913Hx07dvRzysDLzs7myy+/ZPv27Xz77bfs2rWL5s2b07lzZzp37syVV15JrVq1gh0z\naArrSi3qjLGgg2oA1hZBb5KSkvTiG6UqgRtvvJGDBw+SnJzMzJkzOeecc3xuo3fv3mRkZJCamkpK\nSgqRkZFcdtllAUgbOA6Hg1atWtGqVSsAMjMz+e677/j666+ZMWMG33zzDfXr16dTp04kJCTQsWNH\n/vSnPwU5deDlXnxTmKLOGHOAevnOGP8AWonID+5lPWP0QVpamlXF2aY8NmUBu/LYlAXsyuMty/Tp\n03nuueeYMWMG0dHRZx9YBBHhueeeY+XKlYSFhTF16lQuvvjiIo/74osv8ma1CbbCsmRnZ7N7926+\n/vprduzYwZdffklERAQdOnSgS5cudOzYkRYtWhAS4stdfYWz6femNGeMSilVLk2aNIkDBw4wY8YM\nEhMTfZ45xhjDnXfeSUZGBm+//TbTpk1j5syZNGnSJECJy5bD4SAuLi5vLFZESE9P56uvvuL1119n\n+vTpnDhxgvbt25OQkECnTp249NJLqVKlSpCTB56eMSqlKqycnBxuu+02fvjhBx544AFCQ30/F8jO\nzmbOnDl88MEHxMbG8sgjj9CgQYMApLXP77//ztdff80333zDN998w759+2jdunVeoSzPF/SU+HmM\n7sI4DvjDY/ViXDPeHHAvVwNStDAqpWyUlZVFnz59yMnJYdSoUSXqGszKymLatGl89tln1K5dm9mz\nZ1fKC1cyMjLyiuS3337Lzp07z7igp0OHDuXm51KawrgH14OIi+Ttdg4b2FQYbepjB7vy2JQF7Mpj\nUxawK09xshw/fpyuXbvSsGFDBg4cWKJZbZxOJ1OmTOHbb7+lYcOGPPzww8TGxp61X3kZY/QHzwt6\nduzYUeQFPTb93pR4jFFEGgckURDoValKVV5Vq1Zl3bp1XHnllbz++uvceOONPrcRERFBYmIiDz74\nIH/pCEAAACAASURBVHv27CEpKYkZM2YQFRUVgMTlQ3h4OC1btswrvp4X9CxdupQxY8accUGPDdPW\nlfqq1IrCpjNGpVTw/PLLL7Rv357rr7+eq666qkRtHDp0iAceeIB9+/ZxySWXkJSUhDGG9evXs3Xr\nVrKysqhSpQqXXXYZPXr0ICwszM/fRfnheUHP9u3bSU9P5/vvvw92LKAUXakVhRZGpVSu7777jg4d\nOjBkyJASz6v666+/cv/993Po0CGaNGmC0+nk119/JSfnf0/GCwkJoX79+tx888107drVX/HLrfT0\ndGbOnGnNU0H89TxG5Qe2zRVoUx6bsoBdeWzKAnbl8TXLhRdeWOp5VevVq8fUqVMJDw/nhx9+ID09\n/YyiCK4rYn/55ReeffZZNm7cWKL3Ka2ymre1uJxOZ7AjFIsWRqVUpdO6dWteeeUV5s6dy65du0rU\nRv369Ys1Znb06FFefvllvzwEWZUN7UpVSlVar7zyCnfffXeJ5lVdtWoVTz/99FlnigUJCQlhyJAh\n9OnTp6RRyz3tSlVKqXLgpptuYtq0aSQnJ3Po0CGfjt26dWuxiiK4ulU/+eSTkkRUQaCFsYzZNDYD\nduWxKQvYlcemLGBXntJmGT58OMOHD2fq1KlkZGQU+zhfu0aD0ZWqY4wlo4VRKVXpTZ48mV69ejFz\n5kwyMzOLdYyvc4YW9+xSBZ+OMSqlFK7Cdeutt7J3717uv/9+HI7CZ7n0ZYwxV8uWLenevTtXXHFF\npbu/UccYlVKqnAkJCWH58uVER0fz2GOPUdQf0z169KB+/frFajsqKoqwsDC++OILUlJSGDBgAEuW\nLLGmSKgzaWEsYzaNzYBdeWzKAnblsSkL2JXHn1nCwsJYuXIlR44cYdmyZUXu+7e//a3A+VI9xcbG\nMnz4cJYvX87dd99NXFwcGRkZrFq1ilGjRnHvvfeyfv16Tp486bfvI5eOMZZMpXkeo86VqpQqjqpV\nq/LWW29xxRVXsHLlSq6//nqv+3bp0gUR4eWXX2bfvn1eZ77p0qULAL169aJXr17s2rWLDRs2kJaW\nxo4dO9ixYwfPPPMMHTt2pEePHjRt2rREE52roulcqW46xqiU8tXPP/9M+/btufHGG+nWrVuh+2Zl\nZfHWW2+dMVdqmzZt6NGjR6EX6TidTrZs2cL69ev5+uuv89Y3btyY7t27k5CQQExMjN++p2AqT2OM\nWhiVUsqLHTt20LFjR4YNG0bbtm0D+l7/3969x0dRX/8ffx0CxIBaEEFBoKi03AUVVG5J4IeItcEb\n3lr9lZuKlCItolwEAiq0CBYFqSJSQL9qaSmFIKJCWEH9ef9iuUhb2mpRLooI0hqkhPP7Y3fjEklY\nSHbmhJzn45EHmdnJzjsk2bPzOTOf2bp1Ky+99BL5+fl8+eWXQPTM186dO9OzZ09at25doY8iK1Jh\nrLA9RhFJF5HfiUhERF4XkYvCzpQMS70ZsJXHUhawlcdSFrCVJ5VZmjVrxvLly3n00UfZsGFDUl9z\nvH29Ro0aMWDAAObNm8c999zD+eefz8GDB4lEIowePZpBgwbxhz/8gS+++KLU5zlw4AB5eXmMHz+e\noUOHMn78ePLy8jhw4MBx5SpP3mNMvf7AB6p6g4h8H5gHdAo3knPuRNO+fXsWLlzIDTfcQG5uLmef\nndp7slerVo0uXbrQpUsXduzYwcqVK3n55ZfZtm0b8+fP5+mnn+aiiy6iZ8+enH/++YddVpKfn/+t\nfuc///lP1q1bx/PPP+93+khSaEOpIpIOvAPcqar5sXXVgZlAH2A/8GtVfbCEr68JqKp+JSKtgJmq\n2q2EbX0o1TlXJgsXLmTIkCE88MADSV+mUV4KCwt59913eemll3j77beLit7pp5/OpZdeSo8ePdiw\nYQNz585l7969JT7Pd77zHfr37x9KcaxIQ6mhFMZYUXwWuBK4NKEwPgJkAT8BGgFPA7eq6sJSnqsu\nsAIYrqqRErbxwuicK7NZs2YxadIkJk2axGmnnRZKhs8//5z8/HxeeuklduzYUbQ+PT09qVl7zjrr\nLGbMmHHMM/eUVUUqjIH3GEWkBfAGcHax9TWAgcAwVV2nqnnAFGBIwjb3ichqEVkaW/4+sBIYW1JR\ntMZSbwZs5bGUBWzlsZQFbOUJMsvgwYO59dZbue+++0qcVzXV1w7WqVOH6667jscff5z777+fzMxM\nRCTpqey2b9/Oiy++mNKMJakoPcYwTr7JAlYBHYHEat0WqA68lrDuVaCDxE7FUtWxqtpNVXuLSCNg\nCTBAVZcHE905V9mNGzeOnj17Mnny5KSLUSpUqVKFtm3bMmLECNq0aZP01/mdPo4u8MKoqo+p6l2q\nWvytQ31gt6omnjq1k2ixrHeEp7oXqAlMiR1F/i41icuXtQkGLOWxlAVs5bGUBWzlCTqLiDBjxgya\nN2/OtGnTKCwsPOzxYylS5eVYW0Vh3TT5pJNOCmW/x8rS5Ro1gOJvv+LL6cU3VtXbVbWxqnaPHUXe\nkPKEzjlH9GjtqaeeombNmsyaNeuYC1N5O9Z+YdD9xYrG0uUa+/l2AYwvf1XWJ+/bty9NmjQBoFat\nWrRr167onWa8RxHEcmI/JIz9W85TPJPn+WZ53bp1DBs2LLT9W84zffr00P6e//SnP3HBBRcwdepU\nRowYAcCSJUs455xzio4c4z3HVC43aNCAdevWJXWnDxHhrLPOKloOIh9Ee6P79+8P9e85EokkdfJP\nqDPfiMghoIeq5otIR2ANkKGqB2OPZwPLgZNV9bhvZmbprNRIJFL0A7PAUh5LWcBWHktZwFaesLN8\n/vnndOrUiS5dunD11Vezfv36wIdTDxw4wNChQ/nkk0+Oum2VKlWYOHEibdu2DSDZN7Zt28a4ceMO\nO5M2TOYu1yja+eGFMQPYBVyuqmtij48Feqpq1zLux0xhdM6deLZu3UrHjh3p06fPUedVTZXVq1fz\n5JNPlnodY1paGoWFhaSlpdGvXz969+4d2DRzFelyDTNDqapaICILgFki0o/oyTjDgQHhJnPOudI1\natSIlStX0rVrV2rWrEnHjh0Dz5DMnT769OnDv/71LxYvXsycOXP4y1/+ws9+9jMyMjICz2tZ2Cff\nFD+M+wXwNtHLOWYBuaq6qDx2lJube9hYc1gsZEhkKY+lLGArj6UsYCuPlSzNmzdn+fLlPPbYYwwf\nPpwlS5awZ8+eQDN0796dGTNmMHDgQC644ALOPvtsLrjgAm699VZmzJhBjx496N+/PyNHjiQjI4O1\na9cyfPhwtm7dGkg+C9cxRiIRcnNzS90m1CNGVU0rtlwA9It9lKuj/Uc451xZdejQgYULF6KqzJ07\nl8GDB9OmTRsyMzO56KKLAjkbtFq1auTk5JCTk1Niv7Nz5840btyYyZMns3XrVoYPH86dd95J586d\nU54vbNmx+/JOmDChxG38tlPOOZci+/btY9GiRcydO5f169fTpUsXsrKyaNasmYlbSBUUFDBjxgzW\nrl0LwFVXXUXfvn0Pm5i8vFSkHqMXRuecC8BHH33EggULmDdvHgcPHiQrK4vs7Gzq1TvS/CXBUVXy\n8vKYO3cuhYWFtGrVinvuuYfatWuX634qUmEMu8cYGO8xHpmlPJaygK08lrKArTyWskDJeb773e8y\nduxYtmzZwnPPPUd6ejrDhw9n3LhxrFq1ioKCgnLPksy8rSJC7969iyZG37hxI8OGDWPjxo3lnqei\n9BgrVWG0ct2Vc67yEhE6duzIE088wfbt2xk1ahSbN29mwIABPPzww7z//vtJXahf3lq2bMn06dNp\n3bo1u3fvZsyYMSxdujT0WX3KW3Z29lELow+lOuecATt37uSZZ55h7ty5fPbZZ2RlZdGtWzcaNmwY\naI7CwkLmz5/P4sWLAejatWu5XNJRkYZSvTA655wxf/7zn5k3bx5PP/00devWJTMzk8zMTE455ZTA\nMrz22ms8/PDDFBQU0KhRI0aNGkWjRo2O+/kqUmGsNEOpVlSUfkgYLGUBW3ksZQFbeSxlgfLJc955\n5/HQQw+xbds2HnzwQXbt2sVtt93GlClTePPNNzl48GBSz1OWe0N27tyZadOm0ahRo6JLOl577bWj\nf2EpLPQYk+GF0TnnjKpatSo/+MEP+P3vf8/WrVu55ZZbePnll+nfvz9z5sxhy5YtKe0BNmrUiGnT\nptG1a1cKCgr45S9/WXT26onMh1Kdc66C2bJlC/Pnz2f+/PlUr16dzMxMsrKyqFOnTkr2V/ySjtat\nW3P33Xcf0yUdPpRqkJXLNZxzrqyaNm3Kfffdx4cffsiTTz7JoUOHGDp0KBMnTuSVV14p9yHL+CUd\nDzzwAKeddhobNmxg2LBhbNq0qVz3EwS/XCOBlcs1rBVnS3ksZQFbeSxlAVt5LGWBYPNUqVKFrKws\n5s2bx/bt2xk2bBjvvfceAwYM4NFHHy33yy1atWrF9OnTadWqFbt372b06NHHtA8LPcZkLteoNIXR\nOedOZDVq1OBHP/oRq1atYtOmTWRnZ7NkyRKWL19ervupXbs2999/P1dddRWFhYU88cQTPPjggymZ\noCAs3mN0zrkT1Jtvvsk111zDrFmzUjL/6bFc0uE9Ruecc6G7+OKLady4Ma+//npKnj8Vl3RY4IUx\nYJW5H3I0lrKArTyWsoCtPJaygK08kUiEkSNHsmTJkpRd1hG/pKNLly5HvKTjwIED5OXl8cgjj7Bt\n2zYuv/xyZsyYYaLfWBIvjM45dwLLycnh4MGDbNiwIWX7yMjI4O6772bgwIGkpaWxePFi7r33XpYt\nW8bQoUOZM2cOGzdu5L///S8rVqzg5z//Oe3ateOpp55KWaay8B6jc86d4B5//HHmzZvHmDFjUr6v\njRs3MmXKFHbv3h3v45W4bd26dZk2bRq33HJLynMV53OlemF0zlViBQUFNG7cmAkTJtC4ceOU72/n\nzp0MHjyYAwcOHHXbZs2a8f7775Oenp7yXIn85BtDLPUfwFYeS1nAVh5LWcBWHktZwFaeeJaMjAx+\n+tOfkpeXF8h+33rrraTnc92yZQtz5sxJcaJj44XROecqgSFDhvD666/zxRdfpHxf77zzTtL3lCws\nLGTZsmUpTnRsKs1Q6vjx48nOzjYx+41zzoVh0KBB7Nmzh5tvvjml+xk9evQx3dmjW7du5OfnpzDR\nNyKRCJFIhAkTJniPsTJ8n845V5otW7bQoUMHZs+eXeYbD5dm/PjxvPfee0lv36tXL1544YWU5TkS\n7zEaYqn/ALbyWMoCtvJYygK28ljKArbyFM/StGlTMjMzWblyZUr32759e6pUSa68pKWl8cMf/jCl\neY6VF0bnnKtERo0axbJly1J6T8XLLruM+vXrJ7Vt06ZNGThwYMqyHI8KO5QqIlWBBUBD4N/Azaq6\nu4RtfSjVOediLrnkErKysujatWvK9rF69WqefPJJ9u7dW+I2devW5aGHHkp5z/NITtSh1BuAj1U1\nE/gdMDLkPM45VyGMHDmSvLy8lE0TB9ETavr3789ZZ531rWHVtLQ0mjVrxrRp00IpikcTWmEUkXQR\nWS8i3RPWVReR2SKyW0S2iciIkr5eVf+Hb4phQ+CIR4vWWOo/gK08lrKArTyWsoCtPJaygK08JWXJ\nycnh66+/ZuPGjSndf/fu3ZkxYwYDBw6kVatWVKtWjV69evHwww/z/vvvhzLjTTKqhrFTEUkHngVa\nFntoKnAx0B1oBDwtIh+p6sIjPY+qHhKRPKADcGkKIzvn3AkjLS2NESNGsGDBAlq3bp3SfVWrVo2c\nnBwuvPBCxo0bF/jZp8cj8B6jiLQAnoktngdcqqr5IlID2AVcoaqrY9uOAS6LDZciIvcBXYB9qto7\n4TnPAZaravMS9uk9RuecSxCfJm7ixIkl3kOxPPn9GEuXBawCOgKJodoC1YHEm3m9CnQQEQFQ1bGq\n2k1Ve4vIbSLy09h2XwGpO8XKOedOMBkZGQwePJilS5eGHcWcwAujqj6mqnepavGbcdUHdqtq4qyz\nO4kWy3pHeKrngJ4isproyTe3pSRwObPUfwBbeSxlAVt5LGUBW3ksZQFbeY6WJchp4gDT92BMZOms\n1BrA18XWxZe/Ne26qn6pqlfGjiCzVLXi3zbaOecCVLduXW688UaWL18edhRTQjn5pgT7+XYBjC9/\nVdYn79u3L02aNAGgVq1atGvXrmje1Pi7qiCWs7OzA91fRcvjyyUvx3mew5fj68L+/7CYJ5m/765d\nu3LHHXdw7bXXctJJJxXNcdqmTRuAcluuU6cOJ510Uqi/r5FIJKkeZ6gX+IvIIaBH7OSbjsAaIENV\nD8YezwaWAyeranJTtR95P37yjXPOlaB37940aNAgpVOz+ck3x2cdcADolLCuK/BuWYqiNcXfbYfN\nUh5LWcBWHktZwFYeS1nAVp5ks8Qv+E/lNHHgPcZjpqoFRKd4myUiHUSkNzAcmF4ez5+bm2vqF9Y5\n56zo1KkTDRs25I033gg7SspFIhFyc3NL3SbsodRCYtcxxpYzgFnAtcCXwFRVLXNh9KFU55wr3eLF\nixkzZgy/+tWviF0hV658KDVJqpoWL4qx5QJV7aeqp6pqw/Iois45546ud+/e7N+/n02bNoUdJXRm\nhlIrC2vDuZbyWMoCtvJYygK28ljKArbyHEuWtLQ07rrrrpRe8O89RueccxVK3759+etf/8rHH38c\ndpRQVdj7MR4LEdHx48cXXdfjnHPuyMaNG8c777zD4MGDy/V5rfQYI5EIkUiECRMmlNhjrDSFsTJ8\nn845V1affvop3/ve95g5cya1a9cut+e1UhjjzJ58UxlZ6j+ArTyWsoCtPJaygK08lrKArTzHk6Ve\nvXpcf/31KZkmznuMzjnnKqQRI0bw4osvVphCVt58KNU559y35OTk0LBhQ6644opyeT4fSnXOOVeh\nBTVNnEVeGANmqf8AtvJYygK28ljKArbyWMoCtvKUJUunTp2oX79+uU4TV1GGZitNYfS5Up1zLnki\nwqhRo1i6dCknUivK/FypQfEeo3POHbvCwkKaNm3KoEGDaNWqVZmey3uMzjnnKrz4NHF5eXlhRwmU\nF8aAWRvOtZTHUhawlcdSFrCVx1IWsJWnPLL069ePzZs3l8s0cd5jdM45V+HVqFGDO+64o1IdNXqP\n0TnnXKni08Q9+uij1KpV67iew3uMzjnnThj16tXjuuuuS8k0cRZ5YQyYpf4D2MpjKQvYymMpC9jK\nYykL2MpTnllGjBjBihUrytQn9B6jc865E0azZs3o1KkT+fn5YUdJOe8xOuecS8qrr77KTTfdxMyZ\nM0lLSzumr/Ueo3POuRNO586dOeOMM3jzzTfDjpJSlaYwWpkSzkKGRJbyWMoCtvJYygK28ljKArby\nlHcWESmaXPx4WOgxJjMlXKUqjNnZ2WHHcM65Cu3qq69m3759fPDBB2FHOS7Z2dk+Vyp4j9E558rT\nzJkzee655xg5cmTSX+M9Rueccyesfv368cEHH/DJJ5+EHSUlKnxhFJHvi8jesHMky1L/AWzlsZQF\nbOWxlAVs5bGUBWzlSVWWmjVrMmjQoGPuNVroMSajQhdGEckAHgQKws7inHOVydChQ1m7di1791aY\n45KkhdZjFJF04B3gTlXNj62rDswE+gD7gV+r6oOlPMds4DHgD6p6TinbeY/ROefK2YABA9i/fz83\n3XTTUbf1HuNRxIris0DLYg9NBS4GugO3A/eKyPUlPMetwDpVfQ844jfnnHMudUaMGMELL7xQYYZI\nkxV4YRSRFsAbwNnF1tcABgLDVHWdquYBU4AhCdvcJyKrRWQp8GOgj4isBs4UkecD+ybKwFL/AWzl\nsZQFbOWxlAVs5bGUBWzlSXWW5s2bc8kll7B69eqktq8oBTSMI8YsYBXQkcOP9NoC1YHXEta9CnQQ\nEQFQ1bGq2k1Ve6tqtqp2V9VuwA5VvSKg/M4552JGjRpFXl4ehYWFYUcpN6Fexygih4AeqpovItcA\nj6lqvYTHmwMbgQaqurOU5/mH9xidcy54qkr79u3p1asXHTt2LHG7itRjrBp0mFLUAL4uti6+nF7a\nF5ZWFOP69u1LkyZNAKhVqxbt2rUrmgknPtzgy77sy77sy8e2/Morr5CTk8OiRYvo2LEj69evB6BN\nmzYARct16tQJNW/882QKs6Ujxj7ArBKOGM9Q1V1l2I+ZI8ZIJFL0A7PAUh5LWcBWHktZwFYeS1nA\nVp6gshw8eJBzzz2XIUOG0KJFiyNus23bNsaNG8eOHTtSnicZ5s5KLcEnQG0RSTyKPZPoUePucCI5\n55w7mqpVq3LXXXcd9+Ti1lg6YswAdgGXq+qa2ONjgZ6q2rWM+zFzxOiccyei//znPzRu3JjJkyfT\noEGDbz1ekXqMZo4YVbUAWADMEpEOItIbGA5ML4/nt3LbKeecOxHVrFmT22+/3fxRY6QC3Haq+GHc\nL4C3iV7OMQvIVdVF5bEjK7edslacLeWxlAVs5bGUBWzlsZQFbOUJOsvQoUNZs2ZNidPEWbiOMTuJ\n206FWhhVNS0+HVxsuUBV+6nqqaraUFXL5WjROedc6p155plce+21vPDCC2FHKRO/H6Nzzrly88EH\nH9ClSxdmz55Nevo3V9p5j9E551yl1KJFCy666CLy8/OPvrFRlaYwWjn5xkKGRJbyWMoCtvJYygK2\n8ljKArbyhJVl5MiR5OXlcejQocPWW+gxVoSTbwJj5eQb55w70WVmZnL66afz1ltvhR3lW5I5+cZ7\njM4558rdwoULuf/++5k0aRLgPUbnnHOV3DXXXMOePXvYvHlz2FGOmRfGgFnqP4CtPJaygK08lrKA\nrTyWsoCtPGFmqVq1KsOHD2fp0qVF6yz0GJPhhdE551xKDBgwgI0bN7J9+/awoxyTStNjHD9+PNnZ\n2X4CjnPOBWjUqFFs2LCBnJwcEz3GSCRCJBJhwoQJJfYYK01hrAzfp3POWbN9+3aaN2/O2LFjmTlz\nZuiFMc5PvjHEUv8BbOWxlAVs5bGUBWzlsZQFbOWxkKV+/fpcffXVrFixwnuMzjnnHMDdd9/NmjVr\nwo6RNB9Kdc45l3K9evVi8+bNPpTqnHPOAYwePZpTTjkl7BhJ8cIYMAtj/oks5bGUBWzlsZQFbOWx\nlAVs5bGUJTMzk6lTp4YdIyleGJ1zzgUi8TZUlnmP0TnnXKXjPUbnnHMuSV4YA2ZpzB9s5bGUBWzl\nsZQFbOWxlAVs5bGUBezlKYkXRueccy5Bpekx+lypzjnnfK7UGD/5xjnnXCI/+cYQa2PslvJYygK2\n8ljKArbyWMoCtvJYygL28pSkatgBykJENgI7Y4uvquq4MPM455yr+CrsUKqInAosVdXsJLb1oVTn\nnHNFTA6liki6iKwXke4J66qLyGwR2S0i20RkRClPcT5QR0RWisgyEWma+tTOOedOdKEURhFJB54F\nWhZ7aCpwMdAduB24V0SuL+FpvgR+qao9gMnAb1MUt1xZG2O3lMdSFrCVx1IWsJXHUhawlcdSFrCX\npySB9xhFpAXwzBHW1wAGAleo6jpgnYhMAYYAC2Pb3Ad0AfYBfYBNAKr6mog0COY7cM45dyILvMco\nIoOApsC9wFdAD1XNF5GOwFqghqoeiG2bBayIrdNizzMMqKeqo0WkLTBdVbuVsE/vMTrnnCtSWo8x\n8CNGVX0s/rnIYZnqA7vjRTFmJ1AdqMc3Z5/G/QZ4SkReAf4L3JaSwM455yoVS9cx1gC+LrYuvvyt\ne5Wo6teqer2qZqlqD1X9W8oTlgNrY+yW8ljKArbyWMoCtvJYygK28ljKAvbylMTSdYz7+XYBjC9/\nVdYn79u3L02aNAGgVq1atGvXrmh6uPgPy5fDXY7zPN9eXrduXej/H1bzrFu3LtT9W8/jy9Hl+Ocf\nfvghRxPqdYwicojDe4xrgAxVPRh7PBtYDpysqofKsB/vMTrnnCti8jrGI1gHHAA6JazrCrxblqLo\nnHPOHQszhVFVC4AFwCwR6SAivYHhwPRwk5Wv4sN0YbOUx1IWsJXHUhawlcdSFrCVx1IWsJenJGH3\nGIuPb/4CmAWsInoBf66qLiqPHeXm5pLtt51yzrlKLRKJHLVAV9i5Uo+F9xidc84lqig9Rueccy50\nXhgDZm2M3VIeS1nAVh5LWcBWHktZwFYeS1nAXp6SeGF0zjnnElSaHuP48eP95BvnnKvk4iffTJgw\nocQeY6UpjJXh+3TOOZccP/nGEGtj7JbyWMoCtvJYygK28ljKArbyWMoC9vKUxAujc845l8CHUp1z\nzlU6PpTqnHPOJanSFMbc3FwT49sWMiSylMdSFrCVx1IWsJXHUhawlcdSFrCRJxKJkJubW+o2laow\nWrhUI36vNiss5bGUBWzlsZQFbOWxlAVs5bGUBWzkyc7O9sJozZ49e8KOcBhLeSxlAVt5LGUBW3ks\nZQFbeSxlAXt5SuKF0TnnnEvghTFgH374YdgRDmMpj6UsYCuPpSxgK4+lLGArj6UsYC9PSSrN5Rph\nZ3DOOWdLpZ4SzjnnnEuWD6U655xzCbwwOueccwm8MAZMRNJFZL2IdA8xwzkislREdovIv0RkqohU\nDzFPMxF5WUT2icg/ReSusLIkEpEnRCQ/5Aw3isghESlM+PePIWWpKiIPichnsY9ZIlItpCw/OcL/\nS/zfhiFlOkNEFonIFyKyVUQmi8gRe1gBZKkjIs+JyOexv6lhIeX41uudiDQWkZdE5N8islFEeoWR\nrTRVww5QmYhIOvAs0DLEDNWAZcB64BLgDOC3gAIjQshTFXgBWAXcDjQHnhWRT1T12aDzJOT6P8AA\nIBJWhphWwB+BO4D4i+z+kLJMBXoDObHlZ4HPgbEhZHmO6O9NXBXgeWCLqn4cQh6AeUA60AmoR/T/\nZxcwLYQsfwJOAnoAtYAFIlKoqjOCClDK691SYAPQHrgSWCQiLVX1o6CyHZWq+kcAH0AL4H9jeRvU\ndgAAB0ZJREFUH4VA95BydCb6wpqRsO4mYFtIeb5L9I8nPWHdIuCxEH9WNYAtwBogP+Tfm0XAuDAz\nxHJ8J/Z70z1h3f8FVoSdLZZlCLAT+E6IGf4N9E5Yngo8H0KOC2KvMU2L/aw+DjDDEV/vgO7Af4Aa\nCdu+DEwM+3co8cOHUoOTRfSoqCPfvPMPw1+AH6hqQbH1tcIIo6ofqepNqvo1gIh0BjKBlWHkiZkE\nrAZeCTFDXEuiP7OwdQH+o6pFQ8uqukBVQx8GE5GTgXHAWFXdG2KUt4Afi0iGiDQAegHvhJDjHOAL\nVd2SsO7PQH0RaRxQhpJe7y4G/ldVv0pY92psOzO8MAZEVR9T1btUNaxhsHiOXYkvbrEeyBCi79pC\nJSIfEz1Ke53okVIYGToC1wKh9zljw97nAjki8jcR2RLrW4XRDz4X+EhEbhKRDSLyoYg8GFaPsZhB\nRI9mnww5x81Ehwf3AR8D24EJIeTYCZwqIjUT1sUL4ulBBCjl9a4+sK3Yup1AKH3hknhhdL8G2gL3\nhB2EaP/qSuBCorkCFSs4c4A7Qz7yiPsekAZ8CVxDtFj/mHB6VqcQPRIZAtxKtB/cB/hVCFmKuw14\nRFULQ87xP0Rf9LsAlwNNCOdn9SbRwvwbEakpIo2AMbHHQjvJLqYG8HWxdV8T7c2a4SffVGIi8jDR\nd9vXqurmsPOo6nvAeyIyHJgnInep6sEAI4wH/qqqoZz1WZyqbhKR2qr6ZWzVehGpAjwjIneq6qEA\n4xwkWhx/rKofAsTOHl4A/CLAHIcRkQuJFuynw8oQy9ER6Ao0UtXtsXW3Ai+LyCRV/SyoLKp6QESu\nAX4H7AW+IFoY2xN9kxWm/cCpxdalA18dYdvQeGGshGLDp3OJnnRzvaouCzFLA+BCVc1LWL2J6Dvb\nU4HdAca5CThTRPbFlqsDaSLypaoW/2MOREJRjPsAqAbUJToEFZRtwMF4UYz5C3CSiNQN8oW/mF7A\nm6q6I6T9xzUEdseLYsy7RI/4vwsE+v+jquuAZiJSj+jfUBvgEPCvIHMcwSfAecXWnUl02NkMH0qt\nnB4CbgSuVtUlIWdpAfxRRBJ7H+2Bz1Q1yKII0RMGWhMdWm4LPAG8Hfs8cCJytYh8GrukJe4CYI+q\nBlkUAf4fUFVEWiWsa0W0n/Z5wFkSXYKNk6T+DtQWkTMS1rUkehnUP4IMIiK1ROQVETldVT+Njbrk\nAO+p6r+DzHIEbwDtRCQjYV2X2HozvDBWMiJyCXAn0WHD92IXJZ9R7A86SK8AG4kOnTYXkR8Ck4H7\ngw6iqltV9R/xD6JDUAWq+s+gs8REiA5hzhaR74nIFcCU2EegYmc4LgV+KyIXiEhXoj+n2QEP6RbX\nmujvT6hibYDXgadEpE3s7+xxYEHQb/BUdQ9wMjAtNpnHjUTPIZgYZI4SvAJ8BMwXkZYicg/RM1Wf\nCDfW4bwwhiPMmduvje1/MtHhsW1EhzG2xfpXgYq9m72CaAF4A/gN8JCqzgw6izWq+gVwGdGhuHeB\nx4BZqhrWCS83Ez3tfxXRSQcWAaNDyhIXHyq04CpgB9FLjf5A9JKfQSFluZ7o8O77RN8ED1DV50PK\nUvR6F3sTdSXRVsA7RH+nrlLVsId4D+N313DOOecS+BGjc845l8ALo3POOZfAC6NzzjmXwAujc845\nl8ALo3POOZfAC6NzzjmXwAujc845l8ALo3MViIisFpHjmsFERP4rIpnlncm5E40XRueccy6BF0bn\nnHMugRdG5yogEfmJiKwVkbGxO3DsEZHpxba5V0R2xB6/tdhj1UVkeuyxXSLyu9gtihCRfiLytYh8\nP7Z8toj8W0RuCe47dC48Xhidq7guInrbrs7AT4EhInIZgIjcBvwcGAB0B37M4X/vk4ne1eAHQCYg\nwDIAVf0tsBZ4JLbtbCBfVZ9K8ffjnAk+ibhzFYiIrCZatP4OPAnUit9jT0TeBRar6v0i8hawTFUn\nxh5rCvwVyCZ6j8kvgItV9f3Y4xnALqCnqr4mIucSvZPGYuByoJWBmwE7Fwg/YnSu4tpV7MazXwLV\nYp+3JHrLIaDofop7Y4vnANWBtSKyT0T2AZ8C6cD3Y9v/HZgE/AgY40XRVSZVj76Jc86oA0dYJyV8\nDvDf2L/xv/tMosU00WcJn7cjep/MbkTvBelcpeBHjM6dmDYAHeILItIIOD22+HegEKirqv9Q1X8Q\nPWJ8iOhNkRGRHKL9xyuAK0XkhwFmdy5UXhidOzE9QvRknD4i0opoP7IQIDb8+gTwqIh0E5HmwFPA\necDfROQU4FFgsqq+DDwI/EZETg7jG3EuaF4YnatYSjtbrugxVX0GGAM8DLwKRIDtCdsOB14EngPe\nBE4CLlXVr4EHgP3AlNi2DxAdtv1luXwHzhnnZ6U655xzCfyI0TnnnEvghdE555xL4IXROeecS+CF\n0TnnnEvghdE555xL4IXROeecS+CF0TnnnEvghdE555xL4IXROeecS/D/ARr1nD353pZfAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111bc3d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ECTz//PMaRqdYKyMjA3d3dz755BOTuwZtTUrJ1KlTqVu3LoGBgXqHU6qsrCzWr19/11qp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\nqIWIqzZxJYmyRaNs0ShbNEnOlk3cfYxV2zevA4YCLwPLgVJ3f64QT1R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abST4Y34H4CNg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\nIpJGhVFERCTN/weTj8jzc1XU5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111e6f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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84GpgOKLc0xJrkMShM2jcfHoS0l5sYfj5+iHyfCv5619n8PWvl7VayEBRlI6L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\nUGOtXWCt3YbohPUJa9x6Di/EC9SGzDB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FH+NbGBdEMnSDHDzoo3//y6ioqCIYDKb4eopX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\nAyVMERGRHChhioiI5EAJU0REJAf/Hy+IuPHwoZ8uAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cb50590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ss.compute(X=XX, f=f, nboot=100, sstype='QPHD')\n",
    "ac.utils.plotters.eigenvalues(ss.eigenvals, ss.e_br)\n",
    "ac.utils.plotters.subspace_errors(ss.sub_br)\n",
    "ac.utils.plotters.sufficient_summary(XX.dot(ss.W1), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now use local linear models to approximate gradients and make the same plots as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ArFmzJuB9Q0l/IEjKArLySMoCsvJIygKy8kjKAjLy6P0MBRszZgwAJ06cIC0tzeE0SikV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f673c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZmspmGj1ny2uGqlYMue2UXRVGrYct9cjPz8+urppiYmJYv34948aNs6urZICE\nhARCQkK4deuW1lEURTNubm6qMOqdlsU6v4X9eu5dmJJNSsnKlSvp0qVLjrNwzUVvr5uUEl9fX0aN\nGsWNGzcYM2YMy5Yt49KlS1pHe4TeXresVDbT2GqPsYjWARTtnDlzhpIlS+Ls7Kx1FKs4cOAAkZGR\nfPDBB1pHsZoLFy6wYcMGUlNT2bp1Kx07diQmJoYvvviCjz/+mNq1a+Pl5cXTTz+NEDmudVYUu6Ou\nGDWmZY8xv4X9eu5dGJvt1q1bbNiwgbFjx1p8CFUPr1tsbCyff/45H3/8MW+99RahoaF07NgRHx8f\nnJ2dmTJlCpcvX2b48OF8/fXXjB8/Hh8fH1JSUjTLrIfXLTcqm2n02GM0hCqMdszX19cu7qghpWTF\nihV079690N9vMiUlhR07djBq1Cjq1q3LmTNneOutt3B0dHzs2OLFizNkyBD++usvPvvsMw4fPszI\nkSPZsWMH8fHxGqRXFH1Qe6XascaNGzN8+PBCXxz379/Pzp07WbRoEUWKFN7uQXBwMF9++SV16tRh\n+fLlNGnSxOhzHDt2jPnz5/PHH3/g6elJ9+7dqVChggXSKvZg3rx5TJgwgV69emkd5TF57ZVaeP+X\nUPIUGxvL33//jaurq9ZRLCoqKoovv/yS2bNnF9qieP36dTZu3Mi1a9dYunQpPXv2NLlf2Lp1a374\n4QcuXrzIwoULGTNmDG3atKFnz57UqlXLzMkVRZ/UUKrGtOoxHj16lAYNGuRZLPTcuzAkm5SS5cuX\n4+XlZdU3ANZ63eLj4/n666+ZNGkSPXv25NSpU3h5eeVZFA39eXN1dWXlypWcP3+e9u3bM2vWLGbP\nns3x48ex1OiLrf+8aUXP2VSPUbEpeS3sLyx+++037t27xyuvvKJ1FLNKS0vD29ubd999l2LFihER\nEcEHH3xgkb0oK1SowLRp07h8+TJDhgzhyy+/ZMKECfj6+pKammr276coeqB6jHbKw8OD559/nrZt\n22odxSIiIyMZN24cc+bMKVRDgKdPn2bDhg2UKFGCVatW8fzzz1v1+6elpbF7927mzp3L33//TY8e\nPfDw8KBkyZJWzaHYBlvtMaorRjuUlpbGsWPHCu0dNaSULFu2jN69exeaohgTE8OyZctYsGABEydO\n5NixY1YvigAODg707NkTf39/fvrpJ6KiohgxYgSbN2/m9u3bVs+jKJagCqPGtOgxnjp1irJly1K+\nfPk8j9P7qU/SAAAgAElEQVRz7yKvbHv37uXBgwf06dPHion+Zc7XLTk5mR9//JExY8bQvHlzzp49\ny8CBAx+7EayhzPnz9vzzz/PTTz9x7Ngxypcvz6hRo1i5ciVXrlwx6Xy2+vOmNT1nUz1GxWbkt7Df\nlt24cYPNmzczduzYHNfu2QopJUeOHGH06NFERUVx7NgxPv30U8qWLat1tMfUrVuXzz//nPPnz9Om\nTRumT5/OnDlziIiIsNhEHUWxJNVjtENvvvkmJUqUoHv37lpHMau0tDSmTp1Kq1atNLtaNIcrV66w\nYcMG7t69y7Jly+jSpYvWkYzy4MEDvv76axYsWECxYsXw8vKibdu2NvdGJTk5maioKKKiooiJieHZ\nZ5/liSee0DqWTbHVHmPhXNil5Mnf35+RI0dqHcPs9uzZQ3Jysi7/ERoiLi6OrVu3cvDgQaZNm8Y7\n77xjk3cAKVmyJCNGjGDYsGHs3LmTuXPnsnnz5syJOiVKlNA6IpC+3CUqKorIyEgiIyMzC2BUVBQ3\nb97kzp07uLi4ULNmTZycnPjqq69444036Ny5s8lD2YptUIVRYz4+Pla9w8adO3f4559/DFrXFx4e\nrtud+7Nnu3btGlu2bOHTTz/V/MrE2NctNTWV33//ne+++46XX36ZU6dOUalSJYtks+bPm4ODA716\n9aJXr14EBAQwb948hg8fTpcuXejWrdtjPW5z/rxJKbl79+4jRS86Oppbt24RGRnJjRs3SEpKokaN\nGjz55JO4urrSokULateuTa1atahVqxbVqlXL/Fny8fGhbNmyDBs2DG9vb0aMGKGbiV16/ndqqz1G\nVRjtzJEjR2jYsKHmxcOc0tLSWLp0KX379qVGjRpaxzFKREQEGzZsoGLFiuzfv5/mzZtrHcki2rZt\ny/bt2zl37hwLFixg1KhRtGvXDi8vL5P+zlJTU4mJicksepGRkdy6dYvo6GgiIyO5efMmxYsXp0aN\nGtSqVQtXV1c6duyYWfRq1apFxYoVjdoh6Nlnn+XYsWOsXr2aadOm4e7uTr9+/dRSlUJI9RjtzPTp\n0zl9+jT9+/fXOorZbN++HX9/f+bMmWMzBT8yMpKvv/6as2fP8tlnn9G3b1+7uu1TVFQUK1asYNWq\nVTRo0AAvLy+aNGmS+RokJSXlOMwZHR3NzZs3iYqKwtnZmZo1a1K7dm1cXV1xdXXNLHpPPvmkRScq\n3bx5k/fee48//viDwYMH07ZtW7v6+zOU6jEqNsHX15cOHTpoHcMkSUlJ7Nu3j8DAQJKTkylatCj1\n69dn9+7dLFq0yCaKYkJCAr/88gu7du1i9OjR7Nmzh1KlSmkdy+oqVarErFmzmDRpEl999RULFiyg\naNGiFClShJs3b3L37l2qVq3Kk08+Se3atWnYsOEjw5w1atSwyE4/hqpSpQrffPMNPj4+jBgxAm9v\nb4YOHYqLi4tmmRTzsZvCOHPmTNzc3KzazzOENXs+aWlpBAUFMXToUIOO11Pvwtvbm23btnH9+nXS\n0tIyHw8ODsbJyYlTp05RrVo1DRP+K6fXTUqJn58fX3/9Ne3btycsLEyTHpW1e9r5KVWqFCNHjmT4\n8OEsW7aM559/nlq1auHi4qKrNzq5vW5ubm6Eh4ezcOFCJkyYQM+ePXn55ZetOmlKT/9Os9Njj9HH\nxyff9bx2M7UqozDas5MnT1KuXDmcnJy0jmIUb29vNmzYwNWrVx8pihliY2PZsGED3t7eGqTL34UL\nF5g2bRp79uzhu+++44cfftDNxA29cHR0pEWLFrRr147q1avrqijmp1ixYkyZMoWQkBBiYmIYO3Ys\nYWFhWsdScuHm5sbMmTPzPMZurhj1yprFOiAggIYNGxp8vB7ehSYlJbFt27Z833nGxsaybds2OnTo\noPkSh4zXLTY2li1btnD06FE++ugjhg8frvl/+Hp+c2jr2WrXrs2uXbvYsWMH77zzDvXr12fQoEE4\nOztbNJse/p3mxtbehGewmytGBfz8/Gzujhr79u3j+vXrBh17/fp19u3bZ+FE+UtJSWHHjh2MGjUK\nV1dXzpw5w8iRIzUviop1eHl5cerUKVq3bs3YsWPZtWuXuhOJjVGFUWPW3CvV398/363gkpKS2Llz\nJzNmzGD06NHMmDGDnTt3kpSUZKWUjzp27FiOw6c5ydgcXUtxcXG88847nDt3Dl9fX1asWJHvnrTW\npNX9Pw1RmLKVLl2a+fPn4+fnx4kTJ5g4cSJnzpyxSDa1V6r5qaFUOxETE8P169fz7G3lNMHl4sWL\nhIaGsnv3bvr27Uvnzp3Nni0xMZGbN29y48YNbty4wfXr1zN/vXr1qlHnSk5ONns+Q0kp+fzzz2nd\nujU///yzmr6v0KRJEw4ePMimTZsYP348rVu3pn///pQpU0braEoeVGHUmLX6KocPH6ZRo0a5Dudl\nTHDJ6R1eWloaV69eZcOGDQBGF0cpJffu3Xuk6GX9/d27d6lUqRIuLi5UrVoVFxcXmjdvjouLC+vW\nrSM0NNTg76Vlf3H//v1ER0ezb98+3RZFW+/jaaUg2YQQDBgwgJ49e/LBBx8watQo+vfvj7u7u1l+\nTlSP0fxUYbQT/v7+1KtXL8fnzDHBJTU1lVu3bj1ytZdRAG/cuAGAi4tL5kejRo1wc3OjatWqVKhQ\nIdeC/dxzz3H8+HGDhlMdHBxo3bp1vsdZwj///MOmTZvw9fXVzV6gir6UL1+e1atXM3To0Myt5YYN\nG6ZmKOuQKowas9a6Mj8/Pzp16pTjc8ZMcLl27RpffPEFNWvWfKQARkVF8cQTTzxy1deuXbvMQli2\nbFmT3h136dKF3bt3GzSkWrVqVU3uRJGcnMzixYv5+OOPadq0qe7WCmalspnGnNlat25NUFAQn3/+\nOdOnT+fFF1+kb9++Jr+hUusYzU8VRjuQmppKUFAQw4cPz/H5wMBAgye4SCk5fPgwxYoVo1q1arRs\n2ZKqVatSpUoVihUrZs7YQPoasX79+rF+/fo8/5E5OTnRr18/TYZSt2zZQr169Xj77bet/r0V2+To\n6Mi7777Lq6++ytixYxk1ahRDhgyhTZs2WkdTUIVRc9Z4h3zixAmcnZ1zvZecsRNWatWqxYgRI8wR\nzSDu7u5IKXPc+cbBwYGqVavSt29f3N3drZYpQ2hoKH5+foSHh2deEev1qgdUNlNZKpuLiwvfffdd\n5h07vL29GTJkCFWqVDH4HHq9WgTVY1R0zN/fP8+F/cZeZWlxVda5c2c6dOjA3r17H9krtXXr1nTp\n0kWTTLGxsSxfvpxvvvmGihUrWv37K4VH586diYiIYMGCBYwfPx4vLy969+6t+WYV9kqtY9SYNdZu\n+fn50aBBg1yfb9WqlcE3XtVygkvRokXp2bMns2bN4n//+x+zZs2iR48emvznIaVk1apVvPHGG3h4\neDzyXGFaj2dN9p6tePHiTJ06leDgYCIjIxk3bhzHjx/P9+vUOkbzU4XRDuS3sL9Lly5UrVrVoHNp\nNcFFb/bu3cv9+/eZO3eu1lGUQsbV1ZU9e/awZMkSVq1axeLFi7l9+7bWseyKKowas3RfJTo6mqio\nKGrWrJnrMRkTXPLrB2g5wSU7Lfsqf//9N99++y1bt27NccKRPfbKzEFl+5cQgt69e3P69GlatmzJ\nmDFj2LNnT45by6keo/mpwljI5bewP4O7uzuDBw/O8X5yDg4OVK9encGDB2sywUVPkpKSWLJkCZ9+\n+qlRG7IriilKly7NggULOHjwIGFhYXzwwQecPXtW61iFniqMGrN07+LQoUO5LuzPrnPnzvTp04e6\ndevSsmVLXF1dadmyJcOGDWP58uUW2Q7OVFr1VTZt2sRTTz3FkCFDcj3G3ntlplLZctesWTP8/PyY\nNGkSc+bMYfXq1cTFxQGqx2gJalZqIefn58eLL75o8PHHjx+nR48eeHh46HrhsBYCAwM5evQoERER\nut3yTSm8hBAMGjQILy8vJk2axKhRoxgwYAAVKlTQOlqho64YNWbJ3kVKSgohISH53lEjQ2pqKmFh\nYbRo0QLQd+/C2tlu377NypUr2bJlS753y1C9MtOobIZxdnZm7dq17Nq1i99//53vv/8+c9tFvVE9\nRkV3wsPDqVy5ssE7+Z8/f57y5curd6DZpKWlsWLFCoYNG5brtnqKYm3PP/88wcHBvP7660yaNInD\nhw9rHanQUIVRY5bsXQQEBOS5fjG7kJCQzKtF0HfvwprZdu3aRVpaGrNmzTLoeK37UXlR2Uyj12xF\nihShVatW7N69m40bN/Lll1+SkpKidaxMttpjVIWxEPP19aV+/foGH5+9MCrp96P84Ycf2Lp1qy6W\nqShKTtq0aUNYWBhxcXFMnz6d6OhorSPZNFUYNWbJ3kVAQIDB/cX4+HguXLhA06ZNMx+z9x5jQkIC\nn332GUuWLKFOnToGf52e+lHZqWymsYVsFSpU4Ndff6Vfv35MmDCB4OBgbYOheoyKzkRGRhITE5Pn\nwv6sIiIiaNCggbqXYBYbN27k+eefp3///lpHURSDODg48OGHH/L999+zatUqvv322xw3BVDypgqj\nxizVu8hY2G/oHqjBwcG0bNnykcfsuccYEBBAeHg4q1evNnpphl77UaCymcrWsrm5uREaGsqVK1f4\n6KOPNNtSTvUYFV3x8/NT/UUT3bp1i9WrV/Pdd9/Z7FCQori4uODt7U2XLl0YP348J06c0DqSzVCF\nUWOW6l34+fkZvGXZjRs3iI+Pp1atWo88bo89xrS0NJYuXcqoUaNo27atSeewhX6UHqlspskrW5Ei\nRZgzZw4bN25k4cKF/PTTTwbflNwcbPWNpSqMhVBycjJhYWEGF8bQ0FCaN29u8LBrYfbLL79QokQJ\npk6dqnUURTGbl156ieDgYCIiIpg7dy737t3TOpKuFZr/CYUQvYUQG7TOYSxL9C6OHz+Oi4sLpUuX\nNuj43IZR7a3HePbsWbZv3863336b76brebG1fpReqGymMTRbzZo18fPz47nnnuP999/nzJkzlg2G\n6jFqSgjxKTBH6xx6ERAQYPDVYmpqKsePH6d58+YWTqVvDx48YPHixaxateqxIWVFKSyKFSvG0qVL\nWbFiBZ988gm7du1CSql1LN3RvDAKIYoLIcKFEJ2zPFZMCLFGCBEjhLgmhJiQz2mOACMtm9QyLNG7\nMGZh/9mzZ6lYsSLOzs6PPWdPPcb169fj7u5Ov379CnwuW+1HaU1lM40p2fr06cORI0fw9/dn0aJF\nxMfHmz8YqsdoEiFEceBboEm2pxYCzwOdgRHAVCFE39zOI6X80WIhbZAxC/vVbNT0NxJnz55l5cqV\nWkdRFKupV68eR44coV69ekyYMIGLFy9qHUk3NCuMQojGwGHANdvjpYChwFgpZaiUcifwKfBulmM+\nFkIcEELssGZmSzB37+LGjRvExsZSvXp1g44PCQl5bP1iBnvoMUZGRrJu3Tq+++47gzdbz09h6Edp\nQWUzTUGylSxZknXr1jF79mxmzJjB77//br5gqB6jKToBfwBtgawrqJ8BigGHsjzmB7QWD1daSymn\nSSndpZRe1gprKwICAmjcuLFBM0zj4uK4dOkSTZpkv2C3D6mpqSxdupTx48fTunVrreMoimb69++P\nn58fe/fuZfny5SQkJGgdSVOaFUYp5RdSyvFSyux/A1WBGCllUpbHbpJeLCtbLaCVmLt3cejQIerV\nq2fQseHh4TRu3JhixYrl+Hxh7zH++OOPlC9fnkmTJpkh0b8KWz/KWlQ205grW5MmTQgKCsLZ2ZlJ\nkybxzz//FPicqsdoPqWAxGyPZXxePLcvklL+KaUcbLFUNuLQoUOqv2iAU6dO8euvv/LNN9+o9ZuK\n8lCZMmXYsmULEydOZMqUKfj6+modSRNFtA6QgwQeL4AZn5s8dWrQoEHUrl0bgHLlytG8efPMd1oZ\nY/RafJ61P1DQ87Vr147jx4/zn//8h/Dw8Myrqox+XPbPQ0JC6N69e67PZzyW2/Nafn7hwgV69epl\n0tcfPXqUVatWsW7dOqpXr272v98lS5bo5ucr++fm/Hkz9+fZM2qdJ+vnoaGhjB07Vjd5sn5u7p+3\nP//8k4YNG7J//3769OnDwYMH6datW+abaGP+vcXGxhIeHo6Tk5Pmr1fG7y9dukR+hB7WsAgh0gAP\nKaW3EKItcBAoKaVMefi8G7AHKCOlNHo/IyGE1MOfMyc+Pj6Zf4EFdezYMf7v//6PxYsX53vs9evX\n+eCDD9i4cWOum2RnLa56U5Bsixcvpk6dOqxdu9bMqdKZ8+/U3FQ209hrttjYWAYMGMCZM2d4//33\ncXFxMerrJ0+ezOzZszPfxOqJEAIpZY7/+elxDCkUSALaZXmsAxBkSlHUO3P+QPv7+9OgQQODjg0J\nCaF58+Z53jlCr0URTM924MABrly5wtKlS82c6F96/Q8UVDZT2Ws2JycnfvnlF4YNG8akSZM4cuSI\n0V9vi3Q3lCqlfCCE+BpYJYR4k/TJOO8DQ7RNpn++vr5GFcb27dtbOJG+3Lhxgy+//BJvb29KlSql\ndRxFsQlCCN577z3atm3Lq6++yqlTp3j99dcpUkR35cNs9HLFmH2c8z3gGOnLOVYBMwvrIv6s498F\nlXEPxvykpKQQHh6e78SbwrSOMSUlhcWLFzNt2jSLb39nzr9Tc1PZTKOyQdu2bQkLCyM2Npbp06dz\n69atfL9GrWMsACmlo5TSO8vnD6SUb0opn5BS1pBSLino95g5c6auf7gL6tq1a9y/f59q1arle+zp\n06dxcXGx2WEOU2zdupVq1aoxZswYraMois2qWLEie/fu5bXXXmP8+PGEhIRoHcloPj4+zJw5M89j\ndDH5xtL0PPnGXH788UcWLVrElClT8j128+bNpKamMnDgQCsk015ERASfffZZ5l1HFEUpOG9vb/73\nv//h4eFB3759c7wjzbx585gwYYKafKNow5iF/aGhoXazfjEuLo6lS5eyceNGVRQVxYw6d+5MaGgo\nly9f5uOPP+bOnTtaRzIbVRg1Zq7hXT8/P4NuNXXv3j0uX75M48aN8z3W1nuMUkpWrVrFK6+8Qrdu\n3ayQKp2eh+xVNtOobDmrWrUqBw4cwNPTk/Hjx3PixIlHnlc9RkUziYmJREREGDQj9fjx4zRt2pSi\nRYtaIZm29u/fz61bt1i4cKHWURSl0CpSpAhz585lw4YNLFiwgJ9//tnm7/GoCqPGzLEGKSQkhJo1\na1KyZEmDjjV0GNWW1zH+888/bNq0iW3btlGiRAkrpUpnr2veCkplM41esnXr1o2goCCOHz/O3Llz\niYuLs9kJfnZTGAvzrNSAgACDrhallHaxP2pycjJLlizh448/pmnTplrHURS7UatWLQ4dOkSrVq14\n7733uHbtmtaRHmPIrFS7Kox6eWeVlTmKta+vL/Xr18/3uGvXrpGWlkaNGjUMOq+t9hi3bNlC3bp1\nefvtt62Y6F96fgOmsplGZTNcsWLFWLZsGcuWLeP69esUL57rvR804ebmlm9hLLxbF9iRw4cP07Vr\n13yPCw4OpkWLFnluA2frQkND8fPzIzw8vFD/ORVF71599VVKlCiBp6en1lGMptYx2rgrV67wzDPP\n8NVXX+VbCD766CPc3d3p0KGDldJZV2xsLO+99x7ffPMNHh4eWsdRFEXH1DrGQiwgIIAmTZrkWxST\nk5M5ceIEzzzzjJWSWVfG0ow33nhDFUVFUQpEFUaNFbQ/cOjQIerWrZvvcadOnaJ69eo88cQTBp/b\nlnqMe/fu5f79+8ydO1ejRP/SW88nK5XNNCqbafScLS+qMNq4Q4cOGbRxeGGejXr58mW+/fZbtm7d\nSrFixbSOoyiKjbObHuOMGTNwc3PT5cxUUyUkJODs7MzXX3+d71q9cePGMWTIEJo1a2aldNaRlJTE\npEmTmDRpEkOHDtU6jqIoOufj44OPjw+zZs3KtcdoN4WxMP45/f39GTx4cL47u8TGxjJ8+HA2b95c\n6Ha8Wb9+PUIIfvzxRzULVVEUg5lt8o0Qor0Q4k0hRFkhRDMhhL4WqNiggozB+/v7G7wN3FNPPWV0\nUdR7jzEwMJCjR49mFke90HNfRWUzjcpmGj1ny4tB6xiFEJWBnUAzoDjwJzAbeFoI8R8p5TnLRVRy\n4+vra1BhzFi/WJjcu3ePdevW8f3331O+fHmt4yiKUogYNJQqhNgKCGAgEAk88/DXTUBxKaX1bl1g\ngsI4lCqlxMXFhU8++STP2ylJKXnzzTeZM2eOQTcxzio2NpaEhASklI98pKWlPfaYtR/38fGha9eu\nzJkzp6AvpaIodiivoVRDd755EegopXyQMWQlpYwTQkwGjpgnpmKMy5cvk5qaSpUqVfI87sqVKzg6\nOlK1alWjzn/lyhXef/99KlSogBACIQQODg6P/ZrTY3kdY+jv8/vczc2NWbNmFeQlVBRFyZGhhTEN\nKJXD41WBBPPFsT8+Pj4mzZQNCAigcePG+fbWMpZpGNuDO3r0KB4eHuzYscPobNbg4+Oj24lEpv6d\nWoPKZhqVzTR6zpYXQyffbAGWCyGeASTwhBDCE1gNbLNUOCV3hw4dol69evkeZ+r6xeDgYNq3b29K\nNEVRFJtmaI+xGDAXeAfIWEGdCqwF3pdSPrBYQjMojOsYW7ZsSb9+/fK8rVJycjKvv/46GzZsoEyZ\nMgaf++7duwwfPpzo6Gir38tQURTFksy+jlEIURKoQ/oQ7EUp5V3zRLWswjb55sGDB1SoUIFNmzbl\neUuXsLAwNm3aZPQd7H18fDh58iR79uwpaFRFURRdKvA6RiFEGSHEauBtKeUJKWUYcEwIseJhsVRM\nZMo6n8DAQGrXrp3vfc5CQkJo2bKl0ecPDg6md+/eul6DpLKZRmUzjcpmGj1ny4uhPcaVQCvS1y9m\neAdoC3xm7lBK3gxd2G9KfzE1NZXg4GC6d+9uajxFURSbZmiP8RbgJqUMz/Z4C2CflLKyhfKZRWEb\nSu3ZsyeNGzemY8eOuR5z+/ZtRo4cyTfffIOjo6PB5z5x4gSbN2/W9a43iqIoBWWOLeFSgbI5PF4M\nw5d8KGYgpeTIkSP53lEjLCyMp59+2qiiCBAUFISXl1dBIiqKotg0QwvjNmCtEMJdCOH08MMNWAP8\naLF0dsDYMfhLly4BUKlSpTyPM3WZRlBQED179jQpmzWpbKZR2UyjsplGz9nyYmhhnAAEA/uAmIcf\nv5O+681Yy0RTchIQEECjRo3yXLAvpTSpMN68eZPY2Fhat25d0JiKoig2y9jlGk8ADYAk4IKUMs5S\nwcypMPUYR44cSWJiIn369Mn1mEuXLjFnzhzWrFlj1Ll3797NvXv32Lx5c0FjKoqi6JpZbjslhCgH\nPE16r7Ei8JwQorMQorN5YlrWzJkzbfayPit/f38aN26c5zEhISE0b97c6HOHhITQq1cvU6MpiqLo\nno+PDzNnzszzGEPXMQ4ErgIHgT+A/Vk+fi9QSiuZOXOmLne9MaZY379/n7Nnz1K3bt08jzNl/WJC\nQgLh4eH85z//MSmbtalsplHZTKOymUaP2dzc3MxTGEm/9+IawElK6ZDtw7hpj4rJAgMDqVOnDsWK\nFcv1mMTERE6dOsXTTz9t1LmPHz/Os88+i5OTU0FjKoqi2DRD1zHGAc2klJcsnsgCCkuPce7cuRw9\nepQhQ4bkekxwcDBbt25l/vz5Rp37888/x93dnfHjxxc0pqIoiu6Zo8e4A3jFfJEUU/j5+eW7440p\ns1GllAQGBmYu01AURbFnhhbGSOATIcQxIcR3Qoivs35YMmBhZ+gYvKEL+0NDQ40ujBcvXqRUqVKP\nFV099gcyqGymUdlMo7KZRs/Z8mLorjVOwLeWDKLk7fz58zg6Oua5sD8mJobo6GiD7tOYVcbVorE3\nM1YURSmMjFrHaKsKQ49x06ZNrF+/Ps8eoLe3N0ePHuWDDz4w6twffPABixcvxtPTs6AxFUVRbEJe\nPUaDrhiFEA5AH6ApkDELVQDFgRZSSvU/qoX5+fnleyVoSn8xNjaWv//+O88NyRVFUeyJoT3GFcAm\noAswBXADBgOjAF+LJLMTho7B+/v759lfTEtLM6m/GBQUROfOnXO8t6Oe+wMqm2lUNtOobKbRc7a8\nGFoYXwNel1K2A84BI4FawA9AvIWyKQ/FxcVx/vz5PBf2X7x4kdKlS1O5snF3AAsODla73SiKomRh\n6DrGRKCelPKKEOJ74Fcp5QYhRFNgt5SytoVzFoit9xgPHDjA6NGjmTt3bq7H/PDDD9y6dYsRI0YY\nfN6UlBQGDhzI6dOncXFxMUdURVEUm2COdYzngYw9xk4Az2X5+goFi2cdtrxXqr+/P/Xr18/zGFP6\niydPnqROnTqqKCqKYjfMtlcqsAD4VgjxX2ArMFAI8TnpfcdDBQlpLba8V6qvry8NGzbM9fmEhATO\nnj3LU089ZdT3DgoKynMYVc9vJFQ206hsplHZTKPHbGbbK1VK+SXgCZyRUv4F9Cb9DhuHgYEFi6nk\nRUrJ0aNH85x4ExERQd26dSlZsqRR5w4KCqJHjx4FjagoilKoGNpjnA4slFLGZ3v8CWCGlPJ9C+Uz\nC1vuMZ45c4ZOnTqxdu3aXI9Zu3YtTk5O9O3b1+DzXrt2jalTp3Ljxg0cHAy++5iiKEqhYNI6RiFE\nEyCj+TQDiBBC3Ml2WFPgLUDXhdGWBQQE5LsNXEhICOPGjTPqvIGBgXTr1k0VRUVRlGzy+l+xMv/e\nc1GQvjRjf7aPT4CFFs5YqOU3Bu/n55fnxJvo6GhiY2PzvUdjdobclFiP/YEMKptpVDbTqGym0XO2\nvORaGKWUPhn3XAT+BirncC/GJ6SUM6wX1/7kt7A/NDSU5s2bG3XlFx8fz8mTJ/Hw8DBHREVRlELF\nqL1ShRAOUso0IYQL0AEIkVKes1g6M7HVHuPdu3dxcXHhm2++oWjRojke8+mnn9KyZUujilxAQAAB\nAWmIxzkAACAASURBVAF4e3ubK6qiKIpNKfA6RiFEGyHEFaCjEKIKEASsB04IIXqbL6qS1dGjR6lf\nv36uRTE1NTXzitEYQUFBeHl5mSOioihKoWPo+NtnwHYgEBgCJAOVgLeBjywTzT7kNQaf38L+Cxcu\nUK5cOSpWrGjw90tLSyMoKMigmxLruT+gsplGZTONymYaPWfLi6GFsQWwQEoZB3gBv0gpE0mfgJP3\nliyKyfz8/PJc2G/Kbjfnz5/HycnJ6Mk6iqIo9sLQdYz/AP8DrpC+PVxXKeXvQohXSF/f6GrZmAVj\niz3GtLQ0nJ2dWb58OeXLl8/xmMmTJ/PKK6/QqlUrg8/77bffUqVKFT777DNzRVUURbE55tgrdQPw\nCxAAnAX+EEK8A3wNrDFLSuURZ86coXTp0rkWxfj4eM6fP0+zZs2MOm9ISIjqLyqKouTB0C3hpgND\ngflAJyllGnATGCalzP2WD0q+chuDz29hf0REBA0aNKBEiRIGf6+YmBiuXr1K+/btC5RND1Q206hs\nplHZTKPnbHnJdeeb7KSUP2f7/Afzx7GcjE3E9biReE58fX2pV69ers+b0l8MCgrCw8Mj11muiqIo\nhZ2Pj0++BTvXHqMQ4jLQQkp56+FSjVybdFLKJwuQ0+JsscfYqFEj3nrrrVyL41tvvcXEiROpU6eO\nweecP38+w4YNY8CAAeaKqSiKYpNM2isVmAbEZfm9bVUWGxYbG8uVK1eoXbt2js/fvHmT+/fv5/p8\nTpKTkwkNDeWll14yT0hFUZRCKq8t4b56uCQDKeXGh5/n+GG9uIVPTpf0R44coUGDBhQpkvP7FlO2\ngYuIiKBRo0ZUqlSpQNn0QmUzjcpmGpXNNHrOlpe87q5xAAOvEqWUnc2WSMHf3z/f/uJzzz1n1Dnz\nuymxoiiKki6vHuOHWT6tTPrtpbaRvvtNMtCS9LWNS6SUHz5+Bv2wtR6jh4cHbdq0oU2bNo89l5qa\nyhtvvMHKlStxdnY26HxSSt5++2127txp9PZxiqIohZFJPUYp5SdZTuANvCOlXJftxH8C7wK6Loy2\nJC0tjaNHjzJo0KAcnz937hwVK1Y0uCgCXL16lZSUFJ555hkzpVQURSm8DG1SPQ/45vB4IOk3K1ZM\nlH0M/q+//sLJyYly5crleLwpyzSOHTtG9+7dESLHN0cGZ9MTlc00KptpVDbT6DlbXgwtjIHAh0KI\nUhkPCCGcgNmAvyWC2av8FvabUhhDQ0NVf1FRFMVAhu6V2gjYA1Qkfa9UAdQDLgEvSSmvWDBjgdlS\nj3HQoEGULFmS7t27P/bc/fv3efPNN9m0aRPFixc36Hz3799nyJAh3Lx5k9KlS5s7rqIoik0ydR1j\nJinlqYfF0RNo/PDhCGC/lDLFPDEVSJ+R+s477+T43PHjx2nUqJHBRRHSrzDbtWuniqKiKIqBDF4I\nJ6VMklLullIufPixVxXFgss6Bn/79m2uXr2a68J9U4ZRg4ODTR5G1XN/QGUzjcpmGpXNNHrOlhfD\nV4grFnfkyBEaNmyIo6Njjs+HhoYaVRhTU1MJDAzMcVhWURRFyZlBPUZbZys9xmnTpnHmzBn69+//\n2HPXr19n0qRJfPXVVwbPLj116hTr1q3j1KlT5o6qKIpi08xxP0bFCnx9fWnYsGGOz2VcLRqz5CIw\nMFDde1FRFMVIBhdGIUQJIcTrQohZQghnIYS7EMLFkuHsQcYYfGpqKkFBQbkWRlP6iwW9KbGe+wMq\nm2lUNtOobKbRc7a8GFQYhRD1gNPAR8BkoBwwHDghhHjWcvHsx8mTJ3F2dsbJyemx51JTUzl+/LhR\n27lFR0cTGRmZ47ZyiqIoSu4MXce4BzgHjAHuAs8AF4HPgaZSyg6WDFlQttBjXLNmDT/88AOjR49+\n7LmTJ0+yevVqli5davD59u7dS1RUFFu3bjVnTEVRlELBHD3GdsCKrNXl4e8XAMaN7yk58vX1pX79\n+jk+Z+owqtrtRlEUxXiGFsY4oGoOjzcDbpsvjv3JGIP39/fPdSs4YwtjYmIiYWFhdO3a1SzZ9Ehl\nM43KZhqVzTR6zpYXQwvjF8BqIUQv0reDayyEGAasAdZbKpy9uHXrFjdv3uTJJ5987Lm4uDguX75M\nkyZNDD5feHg4Tz31lFF34FAURVHSGbol3GwhRCywHCgF7AQigUXAQsvFM5+ZM2fi5uaGm5ub1lEe\n4ebmxu7du2nUqFGOC/vDwsJo0qQJRYsWNficBdntJns2vVLZTKOymUZlM40es/n4+OR7JWvUAn+R\nvoiuFOkFVUgp7xQkoLXoffLNlClTuHjxIq+//vpjz61YsYKaNWsaXOiklIwYMYLffvuNZs2amTuq\noihKoVDgyTdCCBchxD7gYynlfSllLHBKCLFLCFHRnGHtjY+PD4cOHcpx/aKU0uj+4uXLl3F0dKRp\n04LfJlPP/QGVzTQqm2lUNtPoOVtejOkxAmzI8lgHoCjpw6uKiVJTUwkODs6xMF6/fp20tDRq1qxp\n8Pky9kY19qbEiqIoSjpD1zHGAq2llGeyPd4Y8JdSlrdQPrPQ81BqWFgYvXr1YsWKFY89t2vXLi5c\nuJDj2sbcTJ06lblz5/LSSy+ZM6aiKEqhYo51jPcA1xwerw4kmRpMSV+mYa5t4O7du8e5c+d02fBW\nFEWxFYYWxg3AeiHEm0KIZx5+DCJ9qcZGS4WzBz/++CMNGjR47PHk5GQiIiJ4+umnDT5XcHAwHTt2\npGTJkmbJpuf+gMpmGpXNNCqbafScLS8GLdcAZpK+fnEeUOnhY1HAUmC++WPZj4iICF5++eXHHj99\n+jTVqlXLce/U3AQHB9O3b19zxlMURbE7Rt+P8eEs1CQp5V3LRDI/vfYYo6OjqVOnDps3b8bB4dGL\n902bNiGlZMCAAQadKzU1lYEDBxIREUGNGjUsEVdRFKXQyKvHaOgVI0KIVkBTwPHh5wIoDrSQUg4z\nR1B7c+PGDSpWrPhYUYT0/uKbb75p8LlOnTpFzZo1VVFUFEUpIEPXMc4CjgJzgbWkD62uIn3nG3Wz\n4wJISEh47LG7d+9y9erVXPdOzUlQUBA9e/Y0ZzRd9wdUNtOobKZR2Uyj52x5MbSoDQPeklJWA64A\nbkAV4E/goGWi2a+wsDCaNWtm9DZwBbkpsaIoipLO0HWMiUB9KeVlIcTPwP+3d+9xVtX1/sdf7wHB\nS176HVHxUt4yxEzy9gvzMqIp4QXL0kpNLE07J8suZhfMwTKt1KPgw7xlJeUlf9r1mP40mDK1hIHx\nJ/7IRA+iiIgKijjIZT7nj7U2LoaZYc9iz6wF+/18PPaDvda+vWfPsD97fT9rre9dEfHLdJLiWyOi\n8+MNSqKsPcYZM2YwevToNeZZHD9+PLvuuivHHntsVc/z0ksv8Y1vfIP58+d3er5VMzNbXS2OY3we\n2DW9PhPYN72+GHBTq4bynAZuypQpjBw50kXRzKwGqi2MNwB3SBoF/BY4S9IFwDVAa2+FqwdtbW2r\nLT///PM0NDSw/fbbV/0c06dP75Vh1DL3B5wtH2fLx9nyKXO27lQ77dQPJT0PvBkRj0r6CnA28Arw\n2d4MWG8qW4vVnut06dKlzJgxg6OOOqqXk5mZ1YceH8e4Plqfeozjxo3jyCOP5EMf+lBVz/Hoo48y\nefJkHnzwwd6KaWa2walFjxFJZ0uaJqlN0huSHpJ0cu1i2vLly3niiSd6dBq4lpaWmkxKbGZmiWqP\nYxxLcuq33wOfAE4BJgM3SPpC78Xb8GV7jDNnzuRd73oXm2++eVWPjQhaWlqq3nu1p8rcH3C2fJwt\nH2fLp8zZulPtmW++CHwmIn6fWfc7SdOB/wR+UvNkdaine6POnj2bTTbZpMvZOczMrOeqHUrtD8zu\nZP0/geo2b6xT2Zkw8hymceyxx/bapMRlnr7K2fJxtnycLZ8yZ+tOtYVxHMmw6apzlEnaEbgS+F5v\nBKs3ixYt4sUXX+x0Cqqu9NZhGmZm9azawvgNkoP6n5D0qqSXgGeBDwM/lrSycumtoBuqSo+xtbWV\nvffem/79qxvdfu2115g9ezaHHnpor2Urc3/A2fJxtnycLZ8yZ+tOtT3GU3s1hfV4GLWlpYXDDz+c\ngQMH9mIqM7P606PjGCU1RES7pO2AQ4DWiHiq19LVSNmPY7zqqqsYM2YMl112GYMHD67qsVdccQWn\nnXYan/2sz69gZtZT63wco6QPSnoOOFTStsBU4KfADEkn1C5qfZozZw4DBgyouiiuWLGClpYWRo0a\n1cvJzMzqT7U9xiuB35EUxM8BK4BBwL8DF/dOtPrQ1tbW42HUmTNnsttuu7Hddtv1YrJy9wecLR9n\ny8fZ8ilztu5UWxg/APw4It4Ajgd+GxFvAQ8A7+mtcN2RNFDSHZKaJT0s6cAictRCTwvj1KlTvTeq\nmVkvqXY+xueBT5FMUvw0MDIi7pd0InB5ROzSuzE7zfQFYNuIaJK0B/DziDioi/uWtsd43HHHMX/+\nfH72s5+x2WabVfW4c889lzvvvJP999+/lxOamW2YanGu1JtJppt6BHgK+LOk/wBuIZmSKk+ogZIe\nlzQis26ApBvSQ0JekHR+N09xC/Cj9PpGwFt5chRh6dKlTJgwgXPOOYe5c+fS0NDApEmTWLZs2Vof\nO2/ePJYsWcK+++671vuamVnPVVUYI+K7wJkk50s9LCLagfnAWRFxaU9fVNJA4DZgaIebLgf+NzCC\nZFqrsZJO6iLTkoh4U9IgkiI5rqc5ijBx4kSGDRvGV77yFR566CGWL1/OkiVLuOmmm/jSl77EpEmT\nun38lClTGDVqFA0NVZ//Pbcy9wecLR9ny8fZ8ilztu5UexwjEfEbSZsDe0jaBrgnIt7s6QtK2hO4\ntZP1m5IU32MiohVolfQjkvO0/jq9z/eAg4HFEXF8OoR6J/CtiGjuaZa+NnHiRL72ta+xYMGCNW5r\nb29n7ty53HzzzQCMGDFijftA0o/81re+1as5zczqWbU9xi2Bq4FP83YxfQu4Hrgg3RGnuheUzgF2\nB8YCbwJHRsQkScOBB4FNI2JZet/DgHvTddHheXYC/i9wWkRMXctrFt5jXLp0KcOGDePJJ59c6313\n2GEHJkyYwEYbbbTa+jfffJMzzjiDF198seoZOMzMbE216DHeQLJn6pHAFsA7gROAkcD4noSJiOsi\n4usRsbTDTYOBVytFMTUfGABs08lTjQU2A34kabKkO3qSo6/deOONzJo1q6r7zps3j/vuu2+N9Y89\n9hgHHnigi6KZWS+qtjAeA5wREX+NiDci4rWIuA84A/hkjbJsypo70FSW1zjvWUScHRHviogREXF4\nRJR60uR77rmHlSurO5Vse3s7U6ZMWWP9tGnT+nRS4jL3B5wtH2fLx9nyKXO27lTbY5wH/K9O1g8A\nFtUoy1LWLICV5R73MjsaM2YMO++8MwBbbbUVw4YNWzUlSuWX15vL8+bN61HehQsXrrr++OOP097e\nztSpU5kwYUKf5M3qq9fryXJra2up8mSXW1tbS5VnfVmuKEse/71tWMuV67Nnz2ZtuuwxSsoeE3gE\ncA7wHWAKsBLYh2Qv1SsiYsJaX6nz12hn9R7jX4FNImJFensjcA/wjnRP2FzK0GP8yEc+wr333lv1\n/ffdd1/GjXt7R9tZs2ZxzTXXVD0ca2ZmXeuux9jdFuPfOll3cyfrrgJyFcYOWoFlwEEkBRKSE5W3\nrEtRLItRo0Zx//33VzWc2tDQwAEHHLDauqlTp3Lcccf1VjwzM0t12WOMiIYqL/1qESQi2kiOR7xW\n0gGSjge+RlJ413tnnXUWu+++e1X3HTx4MEcfffRq66ZNm9bnp4HrOMRVJs6Wj7Pl42z5lDlbd6qd\nXWPX7i7r8Podxze/SjJU+2fgWqApIu5ah+cvjY033pixY8cyaNCgbu+35ZZbcvLJJ692qMbChQuZ\nO3cuBx98cG/HNDOre9Uex9hOUsSy47GRXtojYkDvxKuNMvQYKyZOnMgll1zCrFmzVhtWbWhoYPDg\nwZx00klrHNx///3389xzz3H33Xf3dVwzsw1S3h5jVseThPcHdgOagEvyR+s7TU1NNDY2rtpTqSin\nnXYaJ510EjfeeCO33347LS0tDB06lAMOOICjjz56jYP6ITnbzZlnnllAWjOzDUtzc/Nah3ir2mLs\n8sHS/sCtEbFH7ifpA2XaYsyaMWMGRx11FDfc0PV52JcvX85nPvMZnnnmmbUOw9Zac3Nz4V8kuuJs\n+ThbPs6WT5mz1eLMN93ZoQbPYV144oknGDJkSJ8XRTOzelVtj/HiTlZvDpxIcjjFR2sdrJbKvMU4\nevRorr766i7vc9NNN7Hffvtx4YUX9mEyM7MNWy16jId0WA6SYw5/AVy5DtmsGxFBS0sLTU1NRUcx\nM6sb1c7HeHiHy4iIGBkRF0bEwrU/g3Wlra2ty9vmzp3LihUr2Gefffow0dvKfAySs+XjbPk4Wz5l\nztadtW4xSjoQeKwytZSkY4GjgJeAmyPihd6NWBtl2Su1J6ZOncoxxxyD1OnWvpmZ9dA67ZUqaRDw\nJ5LppoZGxJOSvk5yftQWYDHwfuCQiPhnDXPX3PraY7zooou46KKL+vyMN2ZmG7q8e6V+n6SPuFta\nFLcELgYeiIgDI+II4KfApTVPbCxZsoQnn3ySI444ougoZmZ1pbvCeAxwfkTMTpdHAhsD12fucydw\nWO9Eqw9d9RinT5/O8OHD2Wyzzfo40dvK3B9wtnycLR9ny6fM2brTXWHcGpiTWT4CWAE8kFn3Cp1M\nImzrbtq0aZxwwglFxzAzqzvd9RifAs5O50psAJ4FZkXE4Zn7nAp8OyKG9knanNa3HmN7eztjxoxh\n2rRpqyZXNjOz2snbY/wFcLWkjwHjSc5wc23mST8A/AC4o4ZZe01TU9N6s1n/1FNPsc0227gompnV\nWHNz81qPDe+uMF4K3AvcAJwMfDci7gSQdDnJnqnTgctqEba3VQ7XKJvOeoxlmZS4zF8knC0fZ8vH\n2fIpY7bGxsb8hTEiVkbE+RGxdUQMiojvZ27+BbBfRIyuHN9otVPEpMRmZpZYp9k11hfrU4/xlVde\n4bzzzmPBggX071/tGfvMzKwnent2DauhKVOm8OEPf9hF0cysIC6MBevYY2xtbS3NYRpl7A9UOFs+\nzpaPs+VT5mzdcWEskWXLltHa2srIkSOLjmJmVrfcYyxQxx5jS0sL9957L4888kjByczMNmzuMbJ+\nHMfY0tLivVHNzHrRuh7HuEEp+3GMlUmJy3D8YkWZv0g4Wz7Olo+z5VPGbOt0HKP1rTlz5iCJvfba\nq+goZmZ1zT3GAmV7jHfddRcDBw7kuuuuKzqWmdkGzz3G9cD06dPdXzQzKwEXxoK1tbWxePFiZs2a\nxeGHH772B/ShMvYHKpwtH2fLx9nyKXO27rgwlsC0adM45JBD2GSTTYqOYmZW99xjLFClx7jLLrvw\niU98grPPPrvoSGZmdcE9xhJrb2+npaWFUaNGFR3FzMxwYSzcs88+yw477MBOO+1UdJQ1lLk/4Gz5\nOFs+zpZPmbN1p24KY1nPfBMR3hvVzKyPVHPmG/cYCzRjxgz23ntvHn74YYYPH150HDOzuuEeY0n1\n69ePrbfemgMPPLDoKGZmlnJhLNCQIUMYP348/fr1KzpKp8o49FzhbPk4Wz7Olk+Zs3XHhbFAkhg8\neHDRMczMLMM9RjMzqzvuMZqZmVXJhbFgZR6Dd7Z8nC0fZ8vH2WrPhdHMzCzDPUYzM6s77jGamZlV\nqW4KY1lPCVfGTBXOlo+z5eNs+Thbz1RzSrj+fROleGt7I8zMbMPX2NhIY2Mj48aN6/I+7jGamVnd\ncY/RzMysSi6MBSvjGHyFs+XjbPk4Wz7OVnsujGZmZhnuMZqZWd1xj9HMzKxKLowFK/MYvLPl42z5\nOFs+zlZ7LoxmZmYZ7jGamVndcY/RzMysSi6MBSvzGLyz5eNs+ThbPs5Wey6MZmZmGe4xmplZ3XGP\nkfJOO2VmZn2nmmmn6qowNjY2Fh1jDWUu1s6Wj7Pl42z5OFvPNDY2ujCamZn1hHuMZmZWd9xjNDMz\nq5ILY8HKOAZf4Wz5OFs+zpaPs9WeC6OZmVmGe4xmZlZ33GM0MzOrkgtjwco8Bu9s+ThbPs6Wj7PV\nngujmZlZhnuMZmZWd9xjNDMzq5ILY8HKPAbvbPk4Wz7Olo+z1Z4Lo5mZWYZ7jGZmVnfcYzQzM6uS\nC2PByjwG72z5OFs+zpaPs9WeC6OZmVmGe4xmZlZ33GMEmpqa1tvNejMzq43m5maampq6vU9dFcbG\nxsaiY6yhzMXa2fJxtnycLR9n65nGxkYXRjMzs55wj9HMzOqOe4xmZmZVcmEsWBnH4CucLR9ny8fZ\n8nG22nNhNDMzy3CP0czM6o57jGZmZlVyYSxYmcfgnS0fZ8vH2fJxttpzYTQzM8twj9HMzOqOe4xm\nZmZVcmEsWJnH4J0tH2fLx9nycbbac2E0MzPLcI/RzMzqjnuMZmZmVXJhLFiZx+CdLR9ny8fZ8nG2\n2nNhNDMzy3CP0czM6o57jGZmZlVyYSxYmcfgnS0fZ8vH2fJxttpzYTQzM8twj9HMzOqOe4xmZmZV\ncmEsWJnH4J0tH2fLx9nycbbac2E0MzPLcI/RzMzqTnc9xv59HaZWJPUHbgF2BN4ATo2IV4tNZWZm\n67v1eSj1ZOD5iDgUuAP4ZsF5cinzGLyz5eNs+ThbPs5We4UVRkkDJT0uaURm3QBJN0h6VdILks7v\n6vER8SveLoY7At5aNDOzdVZIj1HSQOA2YDTw4YiYlK4fDxwGnA7sBPwSOCsift3Nc/0BOCB9nse7\nuI97jGZmtkp3PcY+L4yS9gRuTRffT1oYJW0KvAwcExGT0/t+Bzg6HS5F0veAg4HFEXF85jl3Be6J\niCFdvKYLo5mZrVK2A/wPA/4MDAeyofYBBgAPZdb9DThAkgAi4sKIODwijpf0eUn/kd7vTWBl70ev\nvTKPwTtbPs6Wj7Pl42y11+d7pUbEdZXrab2rGAy8GhHLMuvmkxTLbdLrWbcDEyV9nKTAf75XApuZ\nWV0p9DhGSe3AkelQ6qnApRGxU+b2XYBZwC4RMWcdXsdDqWZmtsr6chzjUmBgh3WV5TfX9cnHjBnD\nzjvvDMBWW23FsGHDaGxsBN7e3Peyl73sZS9vmMuV67Nnz2atIqKwC9AOjEivDweWA/0ztzeSFMWG\ndXydKKvJkycXHaFLzpaPs+XjbPk4Wz5pXei0ZpTpAP9WYBlwUGbdIUBLRLQXE8nMzOpNaXqM6fJP\nSIrhGSQ749wCfC4i7lrH14kif04zMyuXMvcYO1arrwLXkhzO8TrQtK5F0czMrCcKHUqNiH6VrcV0\nuS0izoiILSJix4i4qlav1dTUtFoTtizKmKnC2fJxtnycLR9n65nm5maampq6vU/RW4x9Zm1vhJmZ\nbfgaGxtpbGxk3LhxXd7H8zGamVndKdsp4czMzErLhbFgZRyDr3C2fJwtH2fLx9lqz4XRzMwso256\njBdddNGqpquZmdWn5uZmmpubGTduXHnmYyyCd74xM7Ms73xTYmUeg3e2fJwtH2fLx9lqz4XRzMws\nw0OpZmZWdzyUamZmViUXxoKVeQze2fJxtnycLR9nq726KYxlPYm4mZn1nWpOIu4eo5mZ1R33GM3M\nzKrkwliwMg/vOls+zpaPs+XjbLXnwmhmZpbhHqOZmdUd9xjNzMyq5MJYsDKPwTtbPs6Wj7Pl42y1\nVzeF0ccxmpmZj2NMucdoZmZZ7jGamZlVyYWxYGUe3nW2fJwtH2fLx9lqz4XRzMwswz1GMzOrO+4x\nmpmZVcmFsWBlHoN3tnycLR9ny8fZas+FsWCtra1FR+iSs+XjbPk4Wz7OVnt1UxjLeoD/okWLio7Q\nJWfLx9nycbZ8nK1nqjnAv3/fRCne2t4IMzPb8DU2NtLY2Mi4ceO6vE/dbDGW1ezZs4uO0CVny8fZ\n8nG2fJyt9urmcI2iM5iZWbl0dbhGXRRGMzOzanko1czMLMOF0czMLMOFsWCSBkp6XNKIorMASNpV\n0u8lvSppjqTLJQ0oOleFpPdKul/SYkn/LenrRWfqSNKNkiYVnSNL0icltUtamfn37qJzAUjqL+lK\nSQvSy7WSNipBrtM7ec8q/+5YgnzbSrpL0kJJz0m6VFKnPbO+JunfJN0u6ZX0/+l5RWfqibo5XKOM\nJA0EbgOGFp0FIP0w+iPwOPBBYFvgZ0AA5xcYDUg+QIE/AX8GzgaGALdJmhsRtxUaLiXpCOBzQHPB\nUTraC7gb+AJQ+fBcWlyc1VwOHA8cly7fBrwCXFhYosTtJH9vFQ3AfwGzIuL5YiKt5ufAQOAgYBuS\n9+1l4IoCM1X8FtgYOBLYCrhF0sqImFBsrOq4MBZE0p7ArUXn6OBAYFdgv4hoA/4l6UKS/2iFF0Zg\nB+AfwBcj4i3gGUkPAIeRfCgUStKmwPXA34rO0omhwGMRsaDoIFmStgTOAUZFxN/TdRcBny40GJD+\njb1UWZb0RWBHoBSjO8AhwKcjYiYwU9KtJNkKLYyS9iUp1u+NiFnpuu8APwDWi8LoodTiHEay5TOc\nt7/BF+1Jkg+otg7rtyoiTEcR8WxEfCr9wELSh4BDgQeKTbbKD4DJwF+KDtKJoSS/37I5GFgSEauG\nniPilogYWWCmNUh6B/Bd4MKIeK3oPKlHgVMkbSJpe2AkMLXgTJB8uV5YKYqp/wcMlvSugjL1iAtj\nQSLiuoj4ekSUZTiLiHg5+wGV9iu+CNxfXKrOSXoe+CvwMHBXwXGQNBw4EShjz3MjYDfgOElPSZqV\n9qPK0DveDXhW0qckzZA0W9KPy9Bj7OAckqHnnxYdJONUYH9gMfA8MA/o+nQufWc+sIWkzTLrKgVx\n6wLy9JgLo3XnP4F9gAuKDtKJ44HRwH4kOQuTFpibgC+XaGsi6z1AP+B14GMkxfsUytGL2pxktgA7\ntAAACTdJREFUC+OLwFkkveOPAz8sMlQnPg+Mj4iVRQfJ+BXwAslW90eAnSnH7/QfJIX6J5I2k7QT\n8J30tjJ8GVu7iPCl4AvQDowoOkeHTFcDbwHHFp1lLTlPBtqA/gVmuAT4TWb5e8Ckot+bDhm36LD8\nMZItoIaCc10ArAR2zqw7kWR4tfD3Lc2zH7AC2K7oLJlMw9NMgzPrGoHlwKAS5BtGMnS/AlhA8sVi\nJTC06GzVXLzzja0mHT69GfgUcFJE/LHgSKukfZT9IuIPmdX/n+Rb6BbAq4UES96r7SQtTpcHAP0k\nvR4RWxSUaTUR8XqHVTOBjYBBJENfRXkBWBERszPrngQ2ljQoyrGz0EjgHxHxYtFBMnYEXo2IeZl1\nLSQjA+8mKUaFiYhW4L2StiH5f7k3yQbAnCJzVctDqdbRlcAngY9GxO+KDtPBnsDdkrJ9iv2BBRFR\nVFGEZEeq95EMO+8D3AhMSa8XTtJHJb2UHu5SsS+wKCKKLIoAjwD9Je2VWbcXSd/slWIireGDlG+H\nqqeBd0raNrNuKMmhVc8UEykhaStJf5G0dUS8FBErSA7FmRYRbxSZrVoujLaKpA8CXwYuAqalBxBv\n2+E/X5H+AjwB/FzSEEnHApcC3y8yVEQ8FxHPVC7AQqAtIv67yFwZzSRDWjdIeo+kY4AfpZdCRbLn\n4u+Bn0naV9IhJL/TGyKivdh0q7yP5O+uNCJiGsmOZxMl7Z3+370euKXgL4lExCLgHcAV6QlDPkky\nZH5xkbl6woWxHMpyJvcTSbJcSjLE9QLJnm4vSCr8byX95nkMyYf834GfAFdGxDWFBiu5iFgIHE0y\nxNYCXAdcGxFl2cHlVJLd+f9MchKCu4BvF5podZXhwLI5AXiR5HCl/0NyqNA5hSZ620kkw72PkXzR\n/lxE/Fexkarn2TXMzMwyCt8KMDMzKxMXRjMzswwXRjMzswwXRjMzswwXRjMzswwXRjMzswwXRjMz\nswwXRqsrkvpJGptOv7RU0vOSrpc0qAfP0S7poN7M2dckfUfS5PT66ZJKdU5LSYdJWlmGE03Yhs9/\nZFZvLiOZkeNskumYTiY5wfGfigxVEpWzfdwOfKDIIJ14iGQmibKcJs42YJ5dw+rNGcDn4+0JmZ+T\n9GngaUkHRsSjBWYrhYh4i2TKsdJITwf4UtE5rD54i9HqTQAjskNy6ZRHQ0nO64ikyZJWnfBY0rvT\n4dNdM89zRDoc+4akOyRtmbn/xekQbZukh9MTPFeGA5+TdK6klyW9KGlsNpykCyQ9LektSS9IGpe5\nrSHz3K9J+q2k7TK3j01vWyTpHkm7d/UmpCdh/4ukJZImkZwPtHLbGEnPdcg8RtI8Sa9K+mq6fqak\n1yXd3OG5u8yRvo+nSXosfX/+JmmXKt+79srvTdIOkn4t6RVJCyRNUDJhdGUo+EFJF6aziiySdFVX\n74XZGoqeENIXX/ryAowlmRfuOeAGkqHULTvcZzJwcWb53SSTrO6aLrcDc4EjSaZvegz4eXrbR0mm\nSzokfdw1wHPpbYcBy0hOgP5+4HhgEXB2evspJHMjNgLvIpnctR3YP739eyQzox8N7AHcB9yX3nYu\n8M/0NfYAxgPPAht38h4MIJma6BbgvcCZJFuIk9LbTwfmdMj8h/R5zyeZDPdRkim/Rqe3H9NNjjmV\nHOnP81T6Mw4lmU/ztirfu5UkX+Y3Av4F/JFkiqrDgFnAhEz+t4BbSYbLTyE58fzRRf/9+bJ+XAoP\n4IsvfX0BPpEWv2XpB/WbwNczt3dWGNs7FMYxmdsPTZ9rc+A8khlJdk5ve0daBBoyH+5DMo9tIpmn\njvR+ozpkfQE4Pb0+Hzgjc9uuJFNuKS0+ozO3iWTOvlM6+fmPAV4HNs2sm9hNYVwJvDfz87QDn8k8\nthX4Wnq92xzpY/89c/u5wKz0ejXvXQPJF4o3yHyhIfmyUPkdnJ4Wwndkbm8Bxhb9t+fL+nHxUKrV\nnYi4MyIOB7YGPg48CPwwnd+xWlMy16eR9Ov3AG4DXiPpWf4d+BIwM97eaeS1iPhn5rFTSSZgJiKa\ngZcl/UDSbyTNBrYF+imZnHlQ+lqVn+OZiBgLbEoyxc+vJC2WtJik8O2UZupoT+DpiHizQ47uVOaW\nbEv/ze612gYMlLRZNznek7l/diLd10m2AGHt713FEJJi+lpm3cMks9dXXuflWH1S3OzrmHXLhdHq\nRjqh6+WV5Yh4PSLujoijSbYojqrc1OGhne2ktjJzvV/677KImE8yRDiSZMj080BLphe4osPz9Ks8\nl6QzSeYk3JhkTsIRJEO2kGwNdaWS72Rgn8xlCHB1F49Rh+Xl3Tx/Z7k72zu0uxzjM/fr+LMIoIr3\nrqKNNfVLn2fV76KT+3T8mc065cJo9aQ/8FVJnR2KsJi393qsDMlV7MaaxXKfzPUPkvS0npb0ceAL\nEXF/RJxH0sPbgqRvBvBvknbMPPYA0p1+SA4h+X5EfDUifkkyOe62JPOmvg4sIHMYhaT3SHqR5AP/\nJWD7dCvyGZItvEs65KyYAeye3WGIpFe6TtItuJ7kWE0V713FP9P8W2XWHURSvGet689h5sJodSMi\nppPsRPI7SadK2lnSfpIuI9kZprJ35RTgREn7S9qfpA/YsTD+MN1TcjjJVtn16dDkAOBHkk6U9G6S\n2ekHkvThICliP5W0l6QTSXpsla2pV0j2dt1D0n4kxxO2p48nfZ1xko6UtCfJzilTI2IRcCXwfUmj\nJe0G/IRkC3hmJ2/FA8Bs4GZJe0o6DfhUz97NLvUkR0fVvHeV/P8CfpmOAjSSvDe3RcTCGv0cVsd8\nHKPVm5OAbwLfJtmp5i3gL8AhEfFCep8rgfel6+cCXwF+k3mOAK4g2atzK5ICdgFARNyafqhfDmxH\nsgfmyRHxlKTt08feB/yNZCv1mxFxR/q8XyYpztNJ9j79Qfr6la3EHwJbAr8iKSL3khRW0tfblKRY\nvjN9jqMi4sWOb0BErJD0EeCnJF8CngCuAoZX+R52/JKQXV5bjo6Pzeaq5r0jIkLSCelrPEKyI84v\nSX6n1WY265Ii/Pdi1hckHUay52e/td7ZzArjoVQzM7MMF0YzM7MMD6WamZlleIvRzMwsw4XRzMws\nw4XRzMwsw4XRzMwsw4XRzMwsw4XRzMws438A5P1HsWpUay4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fca3d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sOTkl7RIyUBSl56JbskqXU1FRzeLFz1JfPyVqe/YB4BFgN+IE/9jGq4Q7mSQS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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdd1c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = ac.gradients.local_linear_gradients(XX, f) #Estimated gradients using local linear models\n",
    "\n",
    "ss.compute(df=df, nboot=100)\n",
    "ac.utils.plotters.eigenvalues(ss.eigenvals, ss.e_br)\n",
    "ac.utils.plotters.subspace_errors(ss.sub_br)\n",
    "ac.utils.plotters.sufficient_summary(XX.dot(ss.W1), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see tight trends in the summary plots in each case, which look very similar between the 3 approaches to approximating gradients. Because these trends look so similar between the approaches, it would likely not make much difference which one is used for constructing a response surface for this particular application, though the global linear model does not allow for higher-dimensional subspaces, so you would need to use a global quadratic model or local linear models if you needed a higher-dimensional space. The consistency between these approaches is not guaranteed; you should explore each for your application and decide which fits your needs the best.\n",
    "\n",
    "We now demonstrate the construction of a subspace with direct access to gradients (computed analytically (our case) or using finite differences or adjoint methods). Since active subspaces use normalized input parameters, the gradients must be scaled according to the chain rule; if $x^*$ represents the normalized inputs, then $\\frac{\\partial f}{\\partial x^*} = \\frac{\\partial f}{\\partial x}\\frac{\\partial x}{\\partial x^*}$, and $x^* = 2\\frac{x-l}{u-l}-1\\Rightarrow x = l + \\frac{u-l}{2}(x^* + 1)\\Rightarrow \\frac{\\partial x}{\\partial x^*} = \\frac{u-l}{2}$, where $u$ and $l$ are the upper and lower bounds on the input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ceeedAHTv3p309HQ2b97M7t27eeSRR+jZsye33XYb2dnZjBkzhkWLFlFQUMCi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\nAX9JNlh/mjRrVgeTnYlMBa4gWw/+GPAPCVo6uhL4iru3JO7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbb0550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hjBo1yqxzjhs3juHDh9O8eXNb/ddyRUxMDBMnTmTRokWUKFFC07ZPnz7NypUr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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f6a1910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1ZhsaRjnbs9G9Mx8EXkRqMZsjUSuweO5F6jsXEtvAWthvv7sYMGAVpaVDVG9W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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fd64e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = wing_grad(x) #Analytically computed gradients\n",
    "\n",
    "#Chain Rule\n",
    "df *= (ub - lb)/2.\n",
    "#Additional chain rule factor for going from degrees to radians\n",
    "df[:,3] *= np.pi/180.\n",
    "\n",
    "ss.compute(df=df, nboot=100)\n",
    "ac.utils.plotters.eigenvalues(ss.eigenvals, ss.e_br)\n",
    "ac.utils.plotters.subspace_errors(ss.sub_br)\n",
    "ac.utils.plotters.sufficient_summary(XX.dot(ss.W1), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The summary plot looks very similar to the plots created by approximating gradients with input/output pairs. This is also not guaranteed; having exact gradients will often result in tighter trends in summary plots because you don't have the additional layer of error from approximating gradients.\n",
    "\n",
    "We'll now construct and use a response surface: a function of the active variable(s) that approximates model output. These are fit with least-squares and can be used to integrate, average, or optimize the function $f$. In the case presented here, we see some curvature in the summary plots, so we use a quadratic surface; your summary plots may indicate better fit with linear, cubic, or other models. The code allows for both polynomial and radial-basis surfaces, both of which have constructors that accept the order of the surface (1 $\\rightarrow$ linear, 2 $\\rightarrow$ quadratic, etc.). Each class has an Rsqr ($R^2$) attribute that measures goodness-of-fit and a 'predict' function that takes active variable values and a flag telling whether to compute the response surface's gradient, and returns the predicted value and gradient (the gradient is None if the flag is False or absent)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R^2 value of the response surface is 0.9906\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111e599d0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OToiRLEZ6565GYqYziffxZ/H+c6gJqkPscbv84A0doiXWO9AfIduOO6y1G621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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103c5150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#quadratic polynomial approximation\n",
    "RS = ac.utils.response_surfaces.PolynomialApproximation(2)\n",
    "\n",
    "#Train the surface with active variable values (y = XX.dot(ss.W1)) and function values (f)\n",
    "y = XX.dot(ss.W1)\n",
    "RS.train(y, f)\n",
    "print 'The R^2 value of the response surface is {:.4f}'.format(RS.Rsqr)\n",
    "\n",
    "#Plot the data and response surface prediction\n",
    "plt.figure(figsize=(7, 7))\n",
    "y0 = np.linspace(-2, 2, 200)\n",
    "plt.plot(y, f, 'bo', y0, RS.predict(y0[:,None])[0], 'k-', linewidth=2, markersize=8)\n",
    "plt.grid(True)\n",
    "plt.xlabel('Active Variable Value', fontsize=18)\n",
    "plt.ylabel('Output', fontsize=18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the $R^2$ value and the graph that the response surface is a good fit. We'll demonsrate how to use the response surface to estimate the average and minimum of the quantity of interest. We must first construct an active variable domain (requiring a computed subspace object) and an active variable map (requiring a domain object)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "avdom = ac.domains.BoundedActiveVariableDomain(ss)\n",
    "avmap = ac.domains.BoundedActiveVariableMap(avdom)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we show how to average the quantity of interest against the joint distribution of input parameters using the response surface, and compare this estimate to a Monte Carlo estimate using the full input space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated average using the response surface is 267.84\n",
      "The estimated average using standard Monte Carlo is 268.07 with 95% CI (268.04, 268.10)\n",
      "Active subspaces took 0.1 seconds and MCMC took 5.9 seconds\n"
     ]
    }
   ],
   "source": [
    "#import time for runtime comparison\n",
    "import time\n",
    "\n",
    "tb_as = time.time()\n",
    "\n",
    "#Approximate the average of the quantity of interest by integrating the response surface\n",
    "int_I = ac.integrals.av_integrate(lambda x: RS.predict(x)[0], avmap, 1000)\n",
    "print 'The estimated average using the response surface is {:.2f}'.format(int_I)\n",
    "\n",
    "te_as = time.time()\n",
    "\n",
    "tb_mc = time.time()\n",
    "\n",
    "#Approximate the average using simple Monte Carlo with M replicates\n",
    "M = int(1e7)\n",
    "X = np.random.uniform(-1, 1, (M, 10))\n",
    "X = lb + (ub - lb)/2.*(X + 1)\n",
    "MC_f = wing(X)\n",
    "MC_I = MC_f.sum()/M\n",
    "MCSE = MC_f.std(ddof=1)/np.sqrt(M)\n",
    "print 'The estimated average using standard Monte Carlo is {:.2f} with 95% CI ({:.2f}, {:.2f})'\\\n",
    "    .format(MC_I, MC_I - 1.96*MCSE, MC_I + 1.96*MCSE)\n",
    "    \n",
    "te_mc = time.time()\n",
    "\n",
    "print 'Active subspaces took {:.1f} seconds and MCMC took {:.1f} seconds'\\\n",
    "    .format(te_as - tb_as, te_mc - tb_mc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see very close answers between these methods, which we would expect based on the good fit of the response surface. The Monte Carlo method takes significantly longer to run despite our model being a fairly simple algebraic equation; for models that take many minutes or hours to run, accurate Monte Carlo (or other traditional integration methods) may be infeasible. We now demonstrate the use of the response surface in minimization and compare the response surface result with the results of a scipy optimizer on the full input space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The response surface optimization results are\n",
      ": ystar = 2.2593, fstar = 132.6419\n",
      "\n",
      "The scipy optimization results are:\n",
      "xstar = [ 1.  1.  1.  0.  1.  1. -1.  1.  1.  1.], fstar = 123.2537\n",
      "xstar*W1 = 2.2563\n"
     ]
    }
   ],
   "source": [
    "#Minimize using the response surface\n",
    "ystar, fstar = ac.optimizers.av_minimize(lambda x: RS.predict(x.reshape(1,1))[0], avdom)\n",
    "print 'The response surface optimization results are\\n: ystar = {:.4f}, fstar = {:.4f}\\n'.\\\n",
    "    format(ystar[0,0], fstar[0,0])\n",
    "\n",
    "#Minimize using scipy\n",
    "import scipy.optimize as opt\n",
    "#wing_n takes normalized inputs while wing takes unnormalized inputs\n",
    "wing_n = lambda x: wing(lb + (ub - lb)/2.*(x + 1))\n",
    "scipy_res = opt.minimize(wing_n, np.zeros(10), bounds=(zip(-1*np.ones(10), np.ones(10))))\n",
    "print 'The scipy optimization results are:'\n",
    "print 'xstar = {}, fstar = {:.4f}'.format(scipy_res['x'], scipy_res['fun'][0,0])\n",
    "print 'xstar*W1 = {:.4f}'.format(scipy_res['x'].reshape((1, 10)).dot(ss.W1)[0,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the estimated minima are fairly close and the estimated active-variable minimizers are almost the same. Again, the algebraic nature of our quantity of interest makes traditional methods feasible; if it were more complex, e.g. the numerical approximation of a PDE that takes hours to compute, the scipy optimizers might become infeasible."
   ]
  }
 ],
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